Datasets:

YanJo199
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scientific-papers-sft-v1

task stringclasses 2 values	instruction stringclasses 2 values	input stringlengths 461 1.8k	draft_output stringlengths 44 774	review_status stringclasses 1 value
keywords	Extract the 8 most important technical keywords from the passage.	uorescence at the specific lines highlighted in (b).(d) Histograms of the EMCCD photoelectron counts from individual Cs and Rb sites over 5000 loading shots. The individual Cs and Rb sites are highlighted in (c). The two peaks correspond to the measured intensity from sites with zero atoms, and sites with one atom. Ato...	atoms, fluorescence, sites, light, emccd, two, one, atom	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	in sustaining coherent behavior, they are as long as 25 mm but have an inner diameter less than 20 nm, with separations between tubules on the order of 20 nm. Unlike isolated atomic systems, it is difficult to justify the Markovian approximations under these circumstances. The Born approximations assume the system- ...	in sustaining coherent behavior, they are as long as 25 mm but have an inner diameter less than 20 nm, with separations between tubules on the order of 20 nm. Unlike isolated atomic systems, it is difficult to justify the Markovian approximations under these circumstances. The Born approximations assume the system- ...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Elementary lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Main ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Trotter type algorithms and error representations 10 3.1 The standard and gen...	9 3 Trotter type algorithms and error representations 10 3.1 The standard and generalized Trotter formulae . 10 3.2 Error representations . 10 4 Operator norm error bounds 12 5 Vector norm error bounds 14 6 Application to Schr¨ odinger equation with time-dependent eﬀective mass and fre- quency 19 Accepted in Quantum 20...	pending
keywords	Extract the 8 most important technical keywords from the passage.	ve broadcast and other fundamental problems, such as spanning tree construction, MST, and BFS, with significantly less communication cost (com- pared tom, the number of edges) inarbitrary networksusing the power ofquan- tum communication? Quantum communication advantage.The recent work of [DMP25] gave a partial answer ...	message, complexity, communication, quantum, they, leader, bound, election	pending
keywords	Extract the 8 most important technical keywords from the passage.	usly , they were tackled by means of SOS matrices and Lemma 4.37. In the dual approach, write the matrix𝐺 ∈ ℝ 𝑚×𝑚[𝒙]in the matrix constraint𝐺 ⪰ 0 in terms of a finite family{𝛤𝒌}𝒌 ⊂ ℝ 𝑚×𝑚 of symmetric matrices:𝐺 = ∑𝒌 𝛤𝒌𝒙𝒌. The corresponding localizing (block) matrix𝑀𝑑(𝐺𝒚)is then 𝑀𝑑(𝐺𝒚)𝒊,𝒋 ≔ ∑ �...	matrix, matrices, complex-valued, one, moment, lemma, localizing, problems	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	e target cell must be moved W horizontal cells and H vertical cells. Then, the total steps are roughly W + H + 6min(W, H) + 5 \|W − H\| beats ignoring a small constant. This takes 7√n beats in the worst case, i.e., W =√n, H = √n/2. When one logical cell is loaded from the point SAM, there are two empty cells in the SAM r...	e target cell must be moved W horizontal cells and H vertical cells. Then, the total steps are roughly W + H + 6min(W, H) + 5 \|W − H\| beats ignoring a small constant. This takes 7√n beats in the worst case, i.e., W =√n, H = √n/2.	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	∼ 1/Q(v/c)2, whereQ∼ω 0/δωis the Q-factor of ring res- onators. To implement parallel optical computations in fre- quency band, the width of the involved spectral lines should be much less than the distance between them in the frequency band. Thus, the value ofQis restricted by the conditionδω≪∆ω=ω 02v/c. Letv/c∼10 −5....	∼ 1/Q(v/c)2, whereQ∼ω 0/δωis the Q-factor of ring res- onators. To implement parallel optical computations in fre- quency band, the width of the involved spectral lines should be much less than the distance between them in the frequency band. Thus, the value ofQis restricted by the conditionδω≪∆ω=ω 02v/c.	pending
keywords	Extract the 8 most important technical keywords from the passage.	ﬁnite dimensions, the left action l(a) = a⊗ IB and the right action is r(b) = IA⊗ b. We have a cyclic and separating vector \|ΩΦ⟩ forA∨B and ⟨ΩΦ\|l(a)\|ΩΦ⟩ = ρB◦ Φ(a), ⟨ΩΦ\|r(b)\|ΩΦ⟩ = ρB(b) . (B.70) Here, ρB is the state before the quantum channel and ρB◦ Φ is the state after the channel [44]. Modular theory can be general...	map, state, hilbert, decodable, action, cyclic, separating, quantum	pending
keywords	Extract the 8 most important technical keywords from the passage.	nes show the analytical approximation of the minimum energy gap derived in Eq.(D63). The green dotted lines show the analytic approximation E± n − E± n+1 = 4ϵ2. 5. Minimum energy gap We can approximate the minimum energy gap by differentiating the approximate quantization condition Eq. (D45) with respect to n at a = 0....	energy, minimum, gap, show, approximation, d63, approximate, gives	pending
keywords	Extract the 8 most important technical keywords from the passage.	elderly care systems, and smart technology for healthy longevity. Dr. Chen is a Board Member of the Taiwan Association of Integrated Care and Chair of the Asia Working Group for Sarcopenia. He was an Advisor to various committees in central and local governments and contributed to global forums on age-friendly policy a...	optical, taiwan, national, university, care, medicine, degree, biomedical	pending
keywords	Extract the 8 most important technical keywords from the passage.	uorescence at the specific lines highlighted in (b).(d) Histograms of the EMCCD photoelectron counts from individual Cs and Rb sites over 5000 loading shots. The individual Cs and Rb sites are highlighted in (c). The two peaks correspond to the measured intensity from sites with zero atoms, and sites with one atom. Ato...	atoms, fluorescence, sites, light, emccd, two, one, atom	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	in sustaining coherent behavior, they are as long as 25 mm but have an inner diameter less than 20 nm, with separations between tubules on the order of 20 nm. Unlike isolated atomic systems, it is difficult to justify the Markovian approximations under these circumstances. The Born approximations assume the system- ...	in sustaining coherent behavior, they are as long as 25 mm but have an inner diameter less than 20 nm, with separations between tubules on the order of 20 nm. Unlike isolated atomic systems, it is difficult to justify the Markovian approximations under these circumstances. The Born approximations assume the system- ...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Elementary lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Main ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Trotter type algorithms and error representations 10 3.1 The standard and gen...	9 3 Trotter type algorithms and error representations 10 3.1 The standard and generalized Trotter formulae . 10 3.2 Error representations . 10 4 Operator norm error bounds 12 5 Vector norm error bounds 14 6 Application to Schr¨ odinger equation with time-dependent eﬀective mass and fre- quency 19 Accepted in Quantum 20...	pending
keywords	Extract the 8 most important technical keywords from the passage.	ve broadcast and other fundamental problems, such as spanning tree construction, MST, and BFS, with significantly less communication cost (com- pared tom, the number of edges) inarbitrary networksusing the power ofquan- tum communication? Quantum communication advantage.The recent work of [DMP25] gave a partial answer ...	message, complexity, communication, quantum, they, leader, bound, election	pending
keywords	Extract the 8 most important technical keywords from the passage.	usly , they were tackled by means of SOS matrices and Lemma 4.37. In the dual approach, write the matrix𝐺 ∈ ℝ 𝑚×𝑚[𝒙]in the matrix constraint𝐺 ⪰ 0 in terms of a finite family{𝛤𝒌}𝒌 ⊂ ℝ 𝑚×𝑚 of symmetric matrices:𝐺 = ∑𝒌 𝛤𝒌𝒙𝒌. The corresponding localizing (block) matrix𝑀𝑑(𝐺𝒚)is then 𝑀𝑑(𝐺𝒚)𝒊,𝒋 ≔ ∑ �...	matrix, matrices, complex-valued, one, moment, lemma, localizing, problems	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	e target cell must be moved W horizontal cells and H vertical cells. Then, the total steps are roughly W + H + 6min(W, H) + 5 \|W − H\| beats ignoring a small constant. This takes 7√n beats in the worst case, i.e., W =√n, H = √n/2. When one logical cell is loaded from the point SAM, there are two empty cells in the SAM r...	e target cell must be moved W horizontal cells and H vertical cells. Then, the total steps are roughly W + H + 6min(W, H) + 5 \|W − H\| beats ignoring a small constant. This takes 7√n beats in the worst case, i.e., W =√n, H = √n/2.	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	∼ 1/Q(v/c)2, whereQ∼ω 0/δωis the Q-factor of ring res- onators. To implement parallel optical computations in fre- quency band, the width of the involved spectral lines should be much less than the distance between them in the frequency band. Thus, the value ofQis restricted by the conditionδω≪∆ω=ω 02v/c. Letv/c∼10 −5....	∼ 1/Q(v/c)2, whereQ∼ω 0/δωis the Q-factor of ring res- onators. To implement parallel optical computations in fre- quency band, the width of the involved spectral lines should be much less than the distance between them in the frequency band. Thus, the value ofQis restricted by the conditionδω≪∆ω=ω 02v/c.	pending
keywords	Extract the 8 most important technical keywords from the passage.	ﬁnite dimensions, the left action l(a) = a⊗ IB and the right action is r(b) = IA⊗ b. We have a cyclic and separating vector \|ΩΦ⟩ forA∨B and ⟨ΩΦ\|l(a)\|ΩΦ⟩ = ρB◦ Φ(a), ⟨ΩΦ\|r(b)\|ΩΦ⟩ = ρB(b) . (B.70) Here, ρB is the state before the quantum channel and ρB◦ Φ is the state after the channel [44]. Modular theory can be general...	map, state, hilbert, decodable, action, cyclic, separating, quantum	pending
keywords	Extract the 8 most important technical keywords from the passage.	nes show the analytical approximation of the minimum energy gap derived in Eq.(D63). The green dotted lines show the analytic approximation E± n − E± n+1 = 4ϵ2. 5. Minimum energy gap We can approximate the minimum energy gap by differentiating the approximate quantization condition Eq. (D45) with respect to n at a = 0....	energy, minimum, gap, show, approximation, d63, approximate, gives	pending
keywords	Extract the 8 most important technical keywords from the passage.	elderly care systems, and smart technology for healthy longevity. Dr. Chen is a Board Member of the Taiwan Association of Integrated Care and Chair of the Asia Working Group for Sarcopenia. He was an Advisor to various committees in central and local governments and contributed to global forums on age-friendly policy a...	optical, taiwan, national, university, care, medicine, degree, biomedical	pending
keywords	Extract the 8 most important technical keywords from the passage.	ach could potentially allow for multiple uses (recycling) of the single-issued quantum token, while still benefiting from the information-theoretic protection provided by quan- tum mechanics. In the existing literature, the concept of quantum tokens appears under different names, such as quan- tum money [1, 19, 20], qu...	quantum, quan-, tum, classical, relies, s-money, token, tokens	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	n photon number ns is ϕ Kerr = 2 χtn s = 0 . 16. (a) ns = 4 (low energy, strong nonlinearity χt = 0 . 02). (b) ns = 20 (higher energy, weaker nonlinearity χt = 0 . 004). (c) Wigner negativity volume versus loss after the Kerr interaction: orange curve for case (a), blue curve for case (b). state with higher non-lineari...	n photon number ns is ϕ Kerr = 2 χtn s = 0 . (a) ns = 4 (low energy, strong nonlinearity χt = 0 . (b) ns = 20 (higher energy, weaker nonlinearity χt = 0 .	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	points represent simulations for idealπpulses, while the red points show simulated results obtained using the realisticπpulses employed in our experiment. The black dashed lines indicate linear fits, with the scaling exponents being 1.00 (a), 2.00 (b), 1.00 (c), and 2.00 (d), respectively. which yield (OB − ⟨OB⟩)\|ψ 0⟩=...	points represent simulations for idealπpulses, while the red points show simulated results obtained using the realisticπpulses employed in our experiment. The black dashed lines indicate linear fits, with the scaling exponents being 1.00 (a), 2.00 (b), 1.00 (c), and 2.00 (d), respectively. which yield (OB − ⟨OB⟩)\|ψ 0⟩=...	pending
keywords	Extract the 8 most important technical keywords from the passage.	riments, and point out key diﬀerences with respect to the non-interacting case. The momentum dis- tribution Πt(k) of the system is the Fourier transform of the one-body reduced density matrix (OBRDM) ρt(x, y), Πt(k) = 1 2π ∫ 2π 0 dx ∫ 2π 0 dy eik(x−y)ρt(x, y), (8) with the momentum (in unit of ¯ k) k ∈ Z due to the per...	momentum, distribution, non-interacting, case, system, obrdm, reads, localized	pending
keywords	Extract the 8 most important technical keywords from the passage.	sion has been quantified by exact complementarity relations, which we have derived both for specific and general initial states. These relations establish that initial coherence is not merely beneficial but is a necessary resource for entanglement generation; its absence in any subsystem yields zero entanglement. Furth...	entanglement, quantum, coherence, initial, gravity, phys, relations, degree	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	le the latter does not. Surprisingly, this is false. The following theorem, proven in App. F, holds instead. Theorem 2 (Rni(Q) = Rni(QI)). For every quantum in- strumental assemblage, there exists a Q assemblage with the same non-instrumentality robustness. From a practical viewpoint, the theorem provides a signiﬁ- can...	The following theorem, proven in App. For every quantum in- strumental assemblage, there exists a Q assemblage with the same non-instrumentality robustness. From a practical viewpoint, the theorem provides a signiﬁ- cant computational shortcut in the task of, given a ﬁxed value ofRni, ﬁnding an assemblage with that rob...	pending
keywords	Extract the 8 most important technical keywords from the passage.	ˆa† k↑ ˆa† k+q↓ ! U † R = 1√ 2 1e iφ −e−iφ 1 ˆa† k↑ ˆa† k+q↓ ! UR,q=0 ˆa† x↑ ˆa† x↓ ! U † R,q=0 = 1√ 2 1e iφ −e−iφ 1 ˆa† x↑ ˆa† x↓ ! . The time evolutions of operators in the Heisenberg pic- ture are the inverses of this, i.e. we make use of U † MaWˆa† k↑/↓UMaW = ˆa† −x↑/↓ U † MaWˆa† x↑/↓UMaW = ˆa† k↑/↓ U †...	operators, initial, steps, fig, heisenberg, maw, umaw, then	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	a fermionic environment [42]. Using notation based on the more recent formulation by Gough and James [26], we can deﬁne the most general type of quantum white noise dynamics as follows. (This theory is rather specialized, and most readers would do well to take this deﬁnition, and the remainder of this section, on trust...	Using notation based on the more recent formulation by Gough and James [26], we can deﬁne the most general type of quantum white noise dynamics as follows. (This theory is rather specialized, and most readers would do well to take this deﬁnition, and the remainder of this section, on trust, rather than trying to unders...	pending
keywords	Extract the 8 most important technical keywords from the passage.	ix A: Generation of comb from MPS Let us consider a three dimensional functionf(x, y, z) which is encoded into an MPS of three tensors per di- mension, f(x, y, z) = X λ Aσ1 1,λ1 Aσ2 λ1,λ2 Aσ3 λ2,λ3 Bσ4 λ3,λ4 Bσ5 λ4,λ5 Bσ6 λ5,λ6 C σ7 λ6,λ7 C σ8 λ7,λ8 C σ9 λ8,1 ,(A1) whereλ j denotes the bond indices and sites 1−3 encode...	comb, tensor, mps, bond, three, encode, thexdimension, thea	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	+ ˆσz 2 ˆσz 3 ˆσz 4 + ˆσz 1 ˆσz 3 ˆσz 4 −ˆσz 3 −ˆσz 4 −ˆσz 1 ˆσz 2 ˆσz 3 −ˆσz 1 ˆσz 2 ˆσz 4).(19) In practice, after the VQE optimisation concludes and the optimal parameters(θ⋆,φ ⋆)are found, they are used to evaluate the expectation values of the observablesˆχˆK and ˆKon the quantum hardware. Since both observables a...	+ ˆσz 2 ˆσz 3 ˆσz 4 + ˆσz 1 ˆσz 3 ˆσz 4 −ˆσz 3 −ˆσz 4 −ˆσz 1 ˆσz 2 ˆσz 3 −ˆσz 1 ˆσz 2 ˆσz 4).(19) In practice, after the VQE optimisation concludes and the optimal parameters(θ⋆,φ ⋆)are found, they are used to evaluate the expectation values of the observablesˆχˆK and ˆKon the quantum hardware. Since both observables a...	pending
keywords	Extract the 8 most important technical keywords from the passage.	due to their dependence on the respective cosmo- logical constants, Λ f(R) m and Λ RI m . These findings highlight the potential for testing quantum gravitational theories through observations of black hole radiation spectra, bridging the gap between theoretical predictions and experimental constraints. Finally, we wan...	gup, black, gravity, zero, hawking, temperature, constants, quantum	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ntage in combinatorial optimization as quantum hardware matures. VIII. ACKNOWLEDGEMENTS G.E., R.C., and M.A.M.-D. acknowledge the sup- port from grants MINECO/FEDER Projects, PID2021- 122547NB-I00 FIS2021, MADQuantumCM project funded by Comunidad de Madrid, the Recovery, Trans- formation, and Resilience Plan, NextGener...	ntage in combinatorial optimization as quantum hardware matures. ACKNOWLEDGEMENTS G.E., R.C., and M.A.M.-D. acknowledge the sup- port from grants MINECO/FEDER Projects, PID2021- 122547NB-I00 FIS2021, MADQuantumCM project funded by Comunidad de Madrid, the Recovery, Trans- formation, and Resilience Plan, NextGenerationE...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ez. The one-body density matrix,ρ(z, z ′) =⟨ ˆΨ†(z) ˆΨ(z′)⟩50 is obtained from TWA simulations as ρ(z, z′) = ψ∗(z)ψ(z ′)− 1 2 δ(z, z ′)(7) whereδ(z, z ′)is the delta function, subtracted due to the symmetrically ordered calculation of the correlation in Wigner function theory, and· · ·denotes the stochastic average. Di...	The one-body density matrix,ρ(z, z ′) =⟨ ˆΨ†(z) ˆΨ(z′)⟩50 is obtained from TWA simulations as ρ(z, z′) = ψ∗(z)ψ(z ′)− 1 2 δ(z, z ′)(7) whereδ(z, z ′)is the delta function, subtracted due to the symmetrically ordered calculation of the correlation in Wigner function theory, and· · ·denotes the stochastic average. Diagon...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	U [α(t), β(t)] whose as- sociated time-dependent Hamiltonian H(t) has the Lie algebra su(2) ⊕ su(2) as its dynamical symmetry. In general this time-dependent Hamiltonian H(t) is a lin- ear combination of all angular momenta of this Lie al- gebra. In the Hilbert space of the two pseudospins any pure quantum state, say \|...	U [α(t), β(t)] whose as- sociated time-dependent Hamiltonian H(t) has the Lie algebra su(2) ⊕ su(2) as its dynamical symmetry. In general this time-dependent Hamiltonian H(t) is a lin- ear combination of all angular momenta of this Lie al- gebra. In the Hilbert space of the two pseudospins any pure quantum state, say \|...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ions inaug urated one of the most outstanding revolutionary periods in western thou ght. One of its results was the creation of two physical theories: QM and Rel ativity. But, as Constantin Piron has remarked, these were in the end “two f ailed rev- olutions” [41] for, up to the present, none of these theories has been...	ions inaug urated one of the most outstanding revolutionary periods in western thou ght. One of its results was the creation of two physical theories: QM and Rel ativity. But, as Constantin Piron has remarked, these were in the end “two f ailed rev- olutions” [41] for, up to the present, none of these theories has been...	pending
keywords	Extract the 8 most important technical keywords from the passage.	ial time diminished as power la w with the characteristic exponent 2/α 0 if the perturbation surpasses σh. Then secondly we use a ﬂexible method to get t2 and t3 and the key point is to use ﬁtted local α in terms of some ﬁxed time interval to ﬁnd typical transitive time,here we use the nam e as local α to distinguish i...	time, local, perturbation, transitive, get, xed, smoothing, then	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	CONCLUSION AND OUTLOOK Various exactly solvable models of chaotic quantum many- body dynamics have appeared in the literature in the past years, each with a characteristic shape of information spread- ing and varying degrees of solvability. This research was kickstarted by dual-unitary circuits, in which space-time du-...	CONCLUSION AND OUTLOOK Various exactly solvable models of chaotic quantum many- body dynamics have appeared in the literature in the past years, each with a characteristic shape of information spread- ing and varying degrees of solvability. This research was kickstarted by dual-unitary circuits, in which space-time du-...	pending
keywords	Extract the 8 most important technical keywords from the passage.	nsider the Pearson correlation coeﬃcient to quantify spatial correlations and conclude, that in agreement with a casual inspection of Fig. 6 (a, d) there are no signiﬁcant spatial trends. Using ﬁnite element simulations of the qubit geometry we are able to infer T1 times limited by the loss tan- gents of the aluminium ...	times, qubit, qubits, loss, fig, materials, coherence, spatial	pending
keywords	Extract the 8 most important technical keywords from the passage.	al. [2020], He et al. [2021], and variational quantum algorithm Rakyta and Zimborás [2022a,b], He et al. [2023]. Depending on their performance, various approaches might yield different results, resulting in the need to check the equivalence between their outputs. There are numerous algorithms that can do this, such as...	quantum, algorithm, circuits, classical, simulation, eq-gan, performance, might	pending
keywords	Extract the 8 most important technical keywords from the passage.	g on the inside glass surface and subsequent surface chemistry that eliminates metallic Rb adsorbed on the glass. Loss of a thin layer of Rb adsorbate on the glass is believed to be the cause for Rb pressure loss at higher rf powers. EIT-based plasma diagnostics are performed with cas- cade EIT from the Rb ground state...	eit, probe, mhz, glass, transition, state, through, coupler	pending
keywords	Extract the 8 most important technical keywords from the passage.	ed as σ:=ρ⊕0∈B(H (s) d ⊕H (a) d ) and a time t> 0. The simulation steps are as follows: 12 1. The agent calculates ηsatisfying the quasi- Hermiticity conditionH† PT =ηHPTη−1 with∥η∥= 1. 2. The agent implements the procedure described above to simulate Gηby setting ˜η= ηand for a single copy of σ(Eq. (F1)). 3. The agen...	agent, hpt, procedure, prover, implements, upt, probability, scheme	pending
keywords	Extract the 8 most important technical keywords from the passage.	tant already in the acceleration experiments due to so-called spin-rotation couplin g [51]. In these applications a better understanding of spinning particle at the classical level may be very useful. There are a lot of operators proposed for the position and spin of r elativistic electron, see [4, 34–36, 45, 52]. Whic...	spin, operators, position, classical, pryce, model, electron, conventional	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ve a simple alternative argument which makes use of the R´enyi entropy S∞(λ1, . . . , λN) =− log maxi λi and the inequality S2≥ S∞ [C4]. Namely, deﬀ = exp(S2(λ1, . . . , λN))≥ exp(S∞(λ1, . . . , λN)) = ( max i λi )−1 n→∞ −→ ∞ according to Lemma 41 above, applied to the sequence of states ¯ρ(n) 0 = ∑ i π(n) i ρ(n) 0 π(n...	ve a simple alternative argument which makes use of the R´enyi entropy S∞(λ1, . , λN) =− log maxi λi and the inequality S2≥ S∞ [C4]. , λN)) = ( max i λi )−1 n→∞ −→ ∞ according to Lemma 41 above, applied to the sequence of states ¯ρ(n) 0 = ∑ i π(n) i ρ(n) 0 π(n) i .	pending
keywords	Extract the 8 most important technical keywords from the passage.	bservables of the system, in particular, the covariance matrix elements, will become time-independent, but the cor- responding density matrix operator does not take on the thermal form unless γ approaches zero. We expect the eﬀective temperature deﬁned in (2.7) to have similar dynamical features as any other system obs...	system, temperature, bath, thermal, ective, state, zero, equilibrium	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	SciPost Physics Submission Quantum Walks on Graphs of the Ordered Hamming Scheme and Spin Networks Hiroshi Miki1*, Satoshi Tsujimoto 2, Luc Vinet 3 1 Meteorological College, Asahi-Cho, Kashiwa 277 0852, Japan 2 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Sakyo-Ku, Ky...	SciPost Physics Submission Quantum Walks on Graphs of the Ordered Hamming Scheme and Spin Networks Hiroshi Miki1*, Satoshi Tsujimoto 2, Luc Vinet 3 1 Meteorological College, Asahi-Cho, Kashiwa 277 0852, Japan 2 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Sakyo-Ku, Ky...	pending
keywords	Extract the 8 most important technical keywords from the passage.	be the vacuum \|0⟩ instead of the two-photon state \|ψin⟩. This is done by replacing the ﬁeld operators { ˆA1, ˆB1, ˆA2, ˆB2, ˆC2, ˆD2} in the decomposition of ˆUJK with the single photon modes ˆA′ 1, ˆB′ 1, etc, as given by the expression (4.83) in Sec 4.4. One could then use the identities (4.67) to obtain the same res...	vacuum, state, bob, bogolyubov, operators, single, transformation, photon	pending
keywords	Extract the 8 most important technical keywords from the passage.	-3 10 -2 10 -1 10 0 d (a) (b) FIG. 6. The parametric functiondillustrates fluctuations in the height of the central phase-space features of the compass states under decoherence: (a)p=q= 0, and (b)X 0 = 1.5. curve, which corresponds to a higher number of pho- ton subtractions, decays more slowly than the red curve. Th...	wigner, decoherence, negativity, temporal, fig, states, evolution, features	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ion as in Deﬁnition 14. In Ref. [13] this is also called the GKSL theorem, since the derivation is based on the pioneering works by Gorini, Kossakowski and Sudarshan in Ref. [113], and Lindblad in Ref. [116], which studied the time- independent case in detail. For proofs of the time-dependent case see Refs [22, 121, 15...	[13] this is also called the GKSL theorem, since the derivation is based on the pioneering works by Gorini, Kossakowski and Sudarshan in Ref. [116], which studied the time- independent case in detail. For proofs of the time-dependent case see Refs [22, 121, 153].	pending
keywords	Extract the 8 most important technical keywords from the passage.	l descrip- tion of the potential outside the active dipole is analogous to how a scalar magnetic potential is a useful quantity to describe the magnetic ﬁeld outside a permanent magnet, highlighting that either a magnetic scalar or vector potential can be used. Now by substituting the ﬁelds given in eqns. (12) and (15)...	magnetic, obtain, vector, substituting, law, potential, potentials, impressed	pending
keywords	Extract the 8 most important technical keywords from the passage.	) When E′ = {e1, e2, e3, e4}, with c(e1) = c(e2) = c(e3) = c(e4) = 1, after t = 50 time steps. Two of the elementary links have success probability p1 with cutoffs 5, 15, and the other two links have success probability p2 with cutoffs 10, 20. where E′ ⊆ E and G = (V, E, c) is a graph corresponding to the physical (ele...	elementary, links, link, obtain, expression, success, corresponding, then	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	uantum oracle circuits 𝒜𝜆 with 𝒜𝜆 accepting advice of length 𝑡(𝜆)and an advice family {adv𝜆}𝜆≥1 where \|adv𝜆\| = 𝑡(𝜆), such that for every input 𝑥 of length 𝜆 = \|𝑥\|, • 𝑥 ∈ ℒ yes ⟹ Pr[𝒜𝒪 𝜆 (𝑥,adv𝜆) = 1] ≥2 3 , • 𝑥 ∈ ℒ no ⟹ Pr[𝒜𝒪 𝜆 (𝑥,adv𝜆) = 1] ≤1 3 . If 𝑡(𝜆) = 0then we say ℒ𝒪 ∈ BQP𝒪. Definit...	uantum oracle circuits 𝒜𝜆 with 𝒜𝜆 accepting advice of length 𝑡(𝜆)and an advice family {adv𝜆}𝜆≥1 where \|adv𝜆\| = 𝑡(𝜆), such that for every input 𝑥 of length 𝜆 = \|𝑥\|, • 𝑥 ∈ ℒ yes ⟹ Pr[𝒜𝒪 𝜆 (𝑥,adv𝜆) = 1] ≥2 3 , • 𝑥 ∈ ℒ no ⟹ Pr[𝒜𝒪 𝜆 (𝑥,adv𝜆) = 1] ≤1 3 . If 𝑡(𝜆) = 0then we say ℒ𝒪 ∈ BQP𝒪. Definit...	pending
keywords	Extract the 8 most important technical keywords from the passage.	1 (2005). [9] C. Zhang, H. Yuan, Z. Tang, W. Quan, and J. C. Fang, Inertial rotation measurement with atomic spins: From angular momentum conservation to quantum phase the- ory, Appl. Phys. Rev. 3, 041305 (2016). [10] X. Wu, Z. Pagel, B. S. Malek, T. H. Nguyen, F. Zi, D. S. Scheirer, and H. M¨ uller, Gravity surveys us...	phys, rev, zhang, atomic, uller, sci, adv, scanning	pending
keywords	Extract the 8 most important technical keywords from the passage.	tive laboratories at distant locations, but have set up all kinds of practical arrangements in advance. In particular, they are at rest with respect to the same inertial frame of reference and they have set up accordingly synchronised clocks. They both possess some kind of random number generators and are able to simul...	they, random, chosen, angle, output, settings, outcomes, laboratories	pending
keywords	Extract the 8 most important technical keywords from the passage.	pect to the working distribution in the deterministic context (AB). Let C,D ∈ { 0, 1}. Irrespective of the current context (AB), deﬁne 4 new observables, i.e., 4 Hermitian operators derived from S as SCD = U− 1 CD S U CD. From Eq. ( 100) we have ⟨S⟩AB = Tr(ρABS) = Tr(UABρ00U− 1 ABS) = Tr(ρ00SAB) = ⟨SAB⟩00 = { − 1 if A ...	sab, chsh, because, classical, context, state, quantum, new	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	0.15 0.20 E/c 0.2 0.4 0.6 0.8 1.0 1.2 1.4 S/c=ln(ρ)/c Figure 3 . Full density of states of the averaged Narain theory –U(1) gravity. Blue lines: S1/c and S2/c as functions of e = E/c, where the full density of states (entropy) ofU(1) gravity is S = max( S1, S2). S1 dominates for E < 0 and S2 for E > 0. Brown line: the ...	0.15 0.20 E/c 0.2 0.4 0.6 0.8 1.0 1.2 1.4 S/c=ln(ρ)/c Figure 3 . Full density of states of the averaged Narain theory –U(1) gravity. Blue lines: S1/c and S2/c as functions of e = E/c, where the full density of states (entropy) ofU(1) gravity is S = max( S1, S2).	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ed on exact diagonalization and are performed at half filling. We setJ= 1,V= 0.25, β= ( √ 5−1)/2 and varyδto drive the localization phase transition. Panel (a-c) are the three different type of localiza- tion tensor discussed in the main text, and Panle (d) shows the scaling behavior to confirm the convergence of the n...	ed on exact diagonalization and are performed at half filling. We setJ= 1,V= 0.25, β= ( √ 5−1)/2 and varyδto drive the localization phase transition. Panel (a-c) are the three different type of localiza- tion tensor discussed in the main text, and Panle (d) shows the scaling behavior to confirm the convergence of the n...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ition along a physically real wave spread out in space, for example. We consider the wavenumber k a classical ob- servable since the wavelength is in principle classically measurable. The eigenvalues of the classical Hermitian operators are experimentally verifi- able quantities. 3. The state space of a composite syste...	ition along a physically real wave spread out in space, for example. We consider the wavenumber k a classical ob- servable since the wavelength is in principle classically measurable. The eigenvalues of the classical Hermitian operators are experimentally verifi- able quantities.	pending
keywords	Extract the 8 most important technical keywords from the passage.	e issue arises that the initial states of trajectories\|ψ z(0)⟩are noise de- pendent. Thus, we introduce a normalized trajectory \|φz⟩, defined as \|φz⟩ ≡ \|ψz⟩ Q k 1√coshr k e −tanhr k 2 (z∗ k)2 ,(F3) to satisfy the coincidence of the initial condition \|φz(0)⟩=\|ψ A(0)⟩. Consequently, we obtain ∂ ∂z ∗ k \|ψz⟩= Y k′ 1q coshr...	tanhr, initial, two, coshr, equation, stochastic, case, normalized	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ng time T(S; n, ·, ·, ·, ·, ·); – the running time T(A; n, ·, ·). Moreover ,DeTypeh calculates the description of A′ in polynomial time in that of S and A; in particular , \|A′\|= polyh(\|S\|, \|A\|). • (Linear constraints processor properties) The ouput linea r constraints processor TM L′(n, ·, ·, ·, ·) runs in time poly- n...	ng time T(S; n, ·, ·, ·, ·, ·); – the running time T(A; n, ·, ·). Moreover ,DeTypeh calculates the description of A′ in polynomial time in that of S and A; in particular , \|A′\|= polyh(\|S\|, \|A\|). • (Linear constraints processor properties) The ouput linea r constraints processor TM L′(n, ·, ·, ·, ·) runs in time poly- n...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	hows the gain distri- bution for the three different angles atδ/2π∼5.5 MHz, along with the respective transverse profile in the inset. Figures 3 (a-c) show the gain distribution forθ eff= 3,4.8 and 6 mrad, respectively. Figure (a) shows a gain distri- bution in the probe channel that spreads over modes up ton= 8, going...	hows the gain distri- bution for the three different angles atδ/2π∼5.5 MHz, along with the respective transverse profile in the inset. Figures 3 (a-c) show the gain distribution forθ eff= 3,4.8 and 6 mrad, respectively. Figure (a) shows a gain distri- bution in the probe channel that spreads over modes up ton= 8, going...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	on. For instance, :ˆϕ(x)2: = XZ k,k′ : uk(x)uk′(x)ˆakˆak′ +u ∗ k(x)uk′(x)ˆa† kˆak′ +u k(x)u∗ k′(x)ˆakˆa† k′ +u ∗ k(x)u∗ k′(x)ˆa† kˆa† k′ : = XZ k,k′ uk(x)uk′(x)ˆakˆak′ +u ∗ k(x)uk′(x)ˆa† kˆak′ +u k(x)u∗ k′(x)ˆa† k′ˆak +u ∗ k(x)u∗ k′(x)ˆa† kˆa† k′ 46 = ˆϕ2(x)− XZ k uk(x)u∗ k(x),(1.141) where in the first equali...	For instance, :ˆϕ(x)2: = XZ k,k′ : uk(x)uk′(x)ˆakˆak′ +u ∗ k(x)uk′(x)ˆa† kˆak′ +u k(x)u∗ k′(x)ˆakˆa† k′ +u ∗ k(x)u∗ k′(x)ˆa† kˆa† k′ : = XZ k,k′ uk(x)uk′(x)ˆakˆak′ +u ∗ k(x)uk′(x)ˆa† kˆak′ +u k(x)u∗ k′(x)ˆa† k′ˆak +u ∗ k(x)u∗ k′(x)ˆa† kˆa† k′ 46 = ˆϕ2(x)− XZ k uk(x)u∗ k(x),(1.141) where in the first equality, ...	pending
keywords	Extract the 8 most important technical keywords from the passage.	.37 ns, (c)t= 0.5 ns, (d)t= 0.6 ns, and (e)t= 0.8 ns. 9 0 MaxMin (a) (b) (c) FIG. 5. Magnetic field distribution for magnetic flux excita- tion at frequencyω m incident from the left, showing signifi- cant frequency multiplication in the nonreciprocal supercon- ducting frequency bus. The bus parameters are eΦdc = 0.7 ...	flux, frequency, field, magnetic, distribution, array, fig, multiplication	pending
keywords	Extract the 8 most important technical keywords from the passage.	the RF transition frequency). We present 3 a model to predict the observed behavior of the EIT sig- nal in the presence of BLWGN, and show excellent agree- ment between experimental and model results. II. EXPERIMENT AL SETUP AND NOISE SOURCE A picture of the experimental setup and a block dia- gram of the noise source...	laser, signal, noise, cell, probe, eit, fig, vapor	pending
keywords	Extract the 8 most important technical keywords from the passage.	s {(1, 0, 0), (0, 1, 0), (0, 0, 1), (−1, −1, −1)}. Other geometric arrangements [for which the last vector is diffeomorphic to (1, 1, 1), (1, 1, 0), (−1, −1, 0), (0, 0, 1) or (0 , 0, −1)] imply different choices of καβγ, which will not be addressed here. The first contribution to the right-hand side of Eq. (82) is l j1...	link, spin, network, grasps, spins, node, where, second	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	y of a quantum phase to encode non-local information in terms of how much spread the state becomes in stabilizer space when perturbed by finite-depth non-Clifford circuits. This op- erational concept captures how a phase can “host” dis- tributed magic resources. While conventional phases such as symmetry-broken or para...	y of a quantum phase to encode non-local information in terms of how much spread the state becomes in stabilizer space when perturbed by finite-depth non-Clifford circuits. This op- erational concept captures how a phase can “host” dis- tributed magic resources. While conventional phases such as symmetry-broken or para...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	P)Λ− 1 s (p0), with the constant boost Λ− 1 s (p0) replaced by Λ c(ki). This has the consequence that the constituent spins are deﬁned so that the zero-momentum vector of the many-body system is the standard vector. The constituent spin operators deﬁned in ( 152) have the property that they can be added to the orbital ...	P)Λ− 1 s (p0), with the constant boost Λ− 1 s (p0) replaced by Λ c(ki). This has the consequence that the constituent spins are deﬁned so that the zero-momentum vector of the many-body system is the standard vector. The constituent spin operators deﬁned in ( 152) have the property that they can be added to the orbital ...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	81) Hence, the fusion subcategoriesS(Mf2,Mf3, 1) andS(Mf3,Mf2, 1) can only have Wilson lines as common elements. The trivial Wilson lineW1 is of course a common element. As we saw in section 2.3, a Wilson line,Wπ, is a member of the fusion subcategory,S(Mf2,Mf3, 1), only if the condition χπ(h) :=B(e,h ) deg χπ = deg χπ...	81) Hence, the fusion subcategoriesS(Mf2,Mf3, 1) andS(Mf3,Mf2, 1) can only have Wilson lines as common elements. The trivial Wilson lineW1 is of course a common element. As we saw in section 2.3, a Wilson line,Wπ, is a member of the fusion subcategory,S(Mf2,Mf3, 1), only if the condition χπ(h) :=B(e,h ) deg χπ = deg χπ...	pending
keywords	Extract the 8 most important technical keywords from the passage.	um is known. 5 Discussion and Conclusion The quantum multinomial distribution expresses multiphoton transition probabilities as a coherent average over routing matrices, weighted by the multivariate hypergeometric dis- tribution. The same routing matrices, the same weights, and the same amplitudes appear in the classic...	quantum, classical, multinomial, routing, hypergeometric, distribution, same, interference	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	1,...,j − √ M 2 − κ2 i ∪i=1,...,j √ M 2 − κ2 i ∪ [M, ∞ ), and the equations (7.75) deﬁne the occupation frac- tion νk of the bound states of the central band in the form \|Eb,j \|=M sin ( πνj 2 ) , j = 1, · · ·,l. (7.77) Note that for this type of condensates the occupa- tion fractions are related by ν1 < ν2 < · · ·< νl....	1,...,j − √ M 2 − κ2 i ∪i=1,...,j √ M 2 − κ2 i ∪ [M, ∞ ), and the equations (7.75) deﬁne the occupation frac- tion νk of the bound states of the central band in the form \|Eb,j \|=M sin ( πνj 2 ) , j = 1, · · ·,l. (7.77) Note that for this type of condensates the occupa- tion fractions are related by ν1 < ν2 < · · ·< νl....	pending
keywords	Extract the 8 most important technical keywords from the passage.	VvJv7n9VIdXvkZE0mqqSCLRWHKkY7RLAU0YJISzSeGYCKZuRWRETYRaJNVyYTgLr+8StrnVbderd3VKo3rPI4iHMMJnIELl9CAW2hCCwik8Ayv8GY9WS/Wu/WxaC1Y+cwR/IH1+QNxDJL1</latexit> ⊋ 1 3 Figure 1: The dynamics of our counterexample in phase space. Quantum and classical Gaussian states are uniquely represented by their covariance ellipse. We assum...	classical, state, quantum, time, dynamics, gaussian, dimensions, step	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	and the impact of orbital in comparison to the spin, we calculate the energy scales within the constant interaction model. Zeeman energy,EZ, is given by: EZ =g ∗µBB=g ∗ eℏB 2me where me is the electron mass. The orbital energy,Eorb scale is given by: Eorb =ℏω c = ℏeB m∗ where m∗ = 0 .09 ± 0.002me [25] is the effective ...	and the impact of orbital in comparison to the spin, we calculate the energy scales within the constant interaction model. Zeeman energy,EZ, is given by: EZ =g ∗µBB=g ∗ eℏB 2me where me is the electron mass. The orbital energy,Eorb scale is given by: Eorb =ℏω c = ℏeB m∗ where m∗ = 0 .09 ± 0.002me [25] is the effective ...	pending
keywords	Extract the 8 most important technical keywords from the passage.	tate as the coupling increases. The oﬀ-diagonal elements indicate that the su- perposition of eigenstates \|e1⟩ and \|e4⟩ grows rapidly and thus decoherence does not fully take place in the energy eigenbasis. Both the diagonal and oﬀ-diagonal elements approach the pointer limit predicted by Eq. (8). When the matrix eleme...	coupling, diagonal, elements, pointer, limit, state, steady, system	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	re these completeness results have appeared, they were also included into each of the PhD theses of Vilmart, Ng and Wang [100, 117, 121]. 9.2 W-states and the ZW-calculus The early completeness results of both Oxford and Nancy relied on a translation of the ZX-calculus into the related ZW-calculus. Before we go into th...	re these completeness results have appeared, they were also included into each of the PhD theses of Vilmart, Ng and Wang [100, 117, 121]. 9.2 W-states and the ZW-calculus The early completeness results of both Oxford and Nancy relied on a translation of the ZX-calculus into the related ZW-calculus. Before we go into th...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	nm, which lines up well with the absorption/emission differ- ence of the triplet. The triplet transition is also optically brightest for F − 3 , with a TDM 2 of 7.9 Debye 2, and the ground state triplet is ∼ 250 meV lower in energy than the ground state singlet [62], suggesting this state may be responsible for the exp...	nm, which lines up well with the absorption/emission differ- ence of the triplet. The triplet transition is also optically brightest for F − 3 , with a TDM 2 of 7.9 Debye 2, and the ground state triplet is ∼ 250 meV lower in energy than the ground state singlet [62], suggesting this state may be responsible for the exp...	pending
keywords	Extract the 8 most important technical keywords from the passage.	d. However, the mod el can be motivated by the interaction of nonrelativistic systems with the electromagnetic ﬁeld [19, 39]. The form of (43) then suggests a connection between the UDW defect and t he Wilson lines of the underlying electromagnetic theory. To see this, let us begin by revis iting the origin of the UDW ...	eld, interaction, udw, dipole, function, electromagnetic, atom, vector	pending
keywords	Extract the 8 most important technical keywords from the passage.	+ωk + cosϑk−cos ( (νl−ωk)T−ϑk ) νl−ωk ]} .(S6) Appendix B: Optimization withπ-pulses This appendix formulates the optimization problem of combining globalπ-pulses with gradient–modulation seg- ments in order to realize a target Ising interaction ∑ j,k ΛjkZjZk .(S1) Consider a sequence ofMgradient–modulation seg- ments....	pulses, matrix, diagonal, target, interaction, cos, appendix, optimization	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	ive gates of superconducting qubit architectures are provided in Fig. 4. Note that above results are incomparable in the sense that Result 2 cannot be decuced form 3 and vice versa. This is because they make statements about hardness of outcome probabilities for diﬀerent fractions of circuits. Formal versions of the ab...	ive gates of superconducting qubit architectures are provided in Fig. Note that above results are incomparable in the sense that Result 2 cannot be decuced form 3 and vice versa. This is because they make statements about hardness of outcome probabilities for diﬀerent fractions of circuits.	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	n through random pulse-intensity variations, and was first successfully demonstrated in [11]. However, while it improves performance, the decoy-state approach relies on conservative assumptions for multi-photon pulses—assuming they are fully compromised—which forces conservative intensity choices, limits maximum transm...	n through random pulse-intensity variations, and was first successfully demonstrated in [11]. However, while it improves performance, the decoy-state approach relies on conservative assumptions for multi-photon pulses—assuming they are fully compromised—which forces conservative intensity choices, limits maximum transm...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	09). [67] P . Wendenbaum, T. Platini, and D. Karevski, Phys. Rev. A 91, 040303 (2015). [68] S. Attal and Y. Pautrat, in Annales Henri Poincar ´e, Vol. 7 (Springer, 2006) pp. 59–104. [69] A. Barchielli, Phys. Rev. A 34, 1642 (1986). [70] A. Barchielli and V . Belavkin, Journal of Physics A: Math- ematical and General 24...	Pautrat, in Annales Henri Poincar ´e, Vol. Belavkin, Journal of Physics A: Math- ematical and General 24, 1495 (1991). Petruccione,The Theory of Open Quan- tum Systems (Oxford University Press, 2007).	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	hin the currently probed phase space, in agreement with the theoretical prediction. These results experimentally corroborate the full hierarchy of quantum correlations in top quarks with discord being the most basic form of quantum correlation, followed by entanglement, steering and Bell correlation. The significance o...	hin the currently probed phase space, in agreement with the theoretical prediction. These results experimentally corroborate the full hierarchy of quantum correlations in top quarks with discord being the most basic form of quantum correlation, followed by entanglement, steering and Bell correlation. The significance o...	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	a real-linear map, it has 1- and (−1)-eigenspacesV + andV −, which one thinks of as the “real” and “imaginary” elements ofC n with respect toc. IfAis ann×ncomplex matrix commuting withc, thenAV + =V +, and ifBis ann×nmatrix whose columns form an orthonormal basis ofV +, thenB †ABis a real matrix. Letι:C 2 →C 2 be the c...	a real-linear map, it has 1- and (−1)-eigenspacesV + andV −, which one thinks of as the “real” and “imaginary” elements ofC n with respect toc. IfAis ann×ncomplex matrix commuting withc, thenAV + =V +, and ifBis ann×nmatrix whose columns form an orthonormal basis ofV +, thenB †ABis a real matrix. Letι:C 2 →C 2 be the c...	pending
keywords	Extract the 8 most important technical keywords from the passage.	ive using Theorem 4.6.2, and obtain d dt D(id ⊗Tt(ρAA′)\|\| id ⊗Rσ(ρAA′)) = d dt H(A)ρA + d dt tr Tt(ρA′) log(Rσ(ρ′ A)) − d dt H(AB)(id ⊗Tt)(ρAA′) = − tr (S − Rσ)(ρA′) log(Rσ(ρA′)) + tr (id ⊗(S − Rσ))(ρAA′) log((id⊗Tt)(ρAA′)) = tr (id ⊗(S − Rσ))(ρAA′) log((id ⊗Tt)(ρAA′)) − 1 ⊗ log(Rσ(ρA′)) = tr (id ⊗...	log, dt2, quantum, second, derivative, mda, channel, expression	pending
summary	Summarize the following scientific passage in 2-4 sentences using clear academic language.	Hall Eﬀect Gyrators and Circulators Giovanni Viola 1 and David P. DiVincenzo 1, 2, 3 1Institute for Quantum Information, R WTH Aachen University, D-52056 Aachen, Germany 2Peter Gr¨ unberg Institute: Theoretical Nanoelectronics, Research Center J¨ ulich 3J¨ ulich-Aachen Research Alliance (JARA), Fundamentals of Future I...	Hall Eﬀect Gyrators and Circulators Giovanni Viola 1 and David P. DiVincenzo 1, 2, 3 1Institute for Quantum Information, R WTH Aachen University, D-52056 Aachen, Germany 2Peter Gr¨ unberg Institute: Theoretical Nanoelectronics, Research Center J¨ ulich 3J¨ ulich-Aachen Research Alliance (JARA), Fundamentals of Future I...	pending
keywords	Extract the 8 most important technical keywords from the passage.	Einstein’s Equivalence principle for superpositions of gravitational fields and quantum reference frames Flaminia Giacomini 1, 2, ∗ and ˇCaslav Brukner 3, 4 1Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada 2Institute for Theoretical Physics, ETH Z ¨urich, Wolfgang-Paul...	quantum, gravitational, eep, reference, physics, vienna, principle, frames	pending