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Geometrical phases have been applied in virtually every major branch of physics and they play an important role in topology and knot theory in mathematics and quantum computation. However, most of the early works focus on pure quantum states which are very unrealistic and almost never occur in practice.
We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling $J$ and find a sequential increase of entanglement depth with growing $J$. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle an...
It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an appropriately defined decay operator.
Inspired by the work done by Belavkin [Belavkin V. P., Stochastics, 1, 315 (1975)], and independently by Mochon, [Phys. Rev. A 73, 032328, (2006)], we formulate the problem of minimum error discrimination of any ensemble of $n$ linearly independent pure states by stripping the problem of its rotational covariance and r...
High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel however degrade entanglement fidelity, thereby increasing the error rates...
Canonical quantum formalism predicts that the interference pattern registered in multi-slit experiments should be a simple combination of patterns observed in two-slit experiments. This has been linked to the validity of Born's rule and verified in precise experiments with photons as well as molecules via nuclear ...
Within the framework of quantum memory channels we introduce the notion of repeatability of quantum channels. In particular, a quantum channel is called repeatable if there exist a memory device implementing the same channel on each individual input.
We extend the well-known static duality \cite{girardeau1960relationship, cheon1999fermion} between 1-D Bosons and 1-D Fermions to the dynamical version. By utilizing this dynamical duality we find the duality of non-equilibrium work distributions between interacting 1-D bosonic (Lieb-Liniger model) and 1-D fermionic (...
Stephen Hawking's discovery of black hole evaporation had the remarkable consequence that information is destroyed by a black hole, which can only be accommodated by modifying the laws of quantum mechanics. Different attempts to evade the information loss paradox were subsequently suggested, apparently without a s...
We report the design, fabrication, and characterization of a microfabricated surface-electrode ion trap that supports controlled transport through the two-dimensional intersection of linear trapping zones arranged in a ninety-degree cross. The trap is fabricated with very-large-scalable-integration (VLSI) techniques w...
Quantum nonlocality may be an artifact of the assumption that observers obey the laws of classical mechanics, while observed systems obey quantum mechanics. I show that, at least in the case of Bell's Theorem, locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the Many-...
Using the process of cavity-enhanced spontaneous parametric down-conversion (SPDC), we generate a narrow-band polarization-entangled photon pair resonant on the rubidium (Rb) D1 line (795 nm). The degenerate single-mode photon pair is selected by multiple temperature controlled etalons.
We investigate the sub-Planck-scale structures associated with the SU(1,1) group by establishing that the Planck scale on the hyperbolic plane can be considered as the inverse of the Bargmann index $k$. Our discussion involves SU(1,1) versions of Wigner functions, and the quantum-interference effect is easily visualiz...
Current benchmarks for mid-circuit measurements (MCMs) are limited in scalability or the types of error they can quantify, necessitating new techniques for quantifying their performance. Here, we introduce a theory for learning Pauli noise in MCMs and use it to create MCM cycle benchmarking, a scalable method for benc...
We compare several quantum phase estimation (QPE) protocols intended for early fault-tolerant quantum computers (EFTQCs) in the context of models of their implementations on a surface code architecture. We estimate the logical and physical resources required to use these protocols to calculate the ground state energy ...
We characterize the algebraic structure of semi-direct product of cyclic groups, $\Z_{N}\rtimes\Z_{p}$, where $p$ is an odd prime number which does not divide $q-1$ for any prime factor $q$ of $N$, and provide a polynomial-time quantum computational algorithm solving hidden symmetry subgroup problem of the groups.
We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for analytical study.
We introduce a spin-based receiver to sensitively detect the electric fields of millimeter (mm) waves by using quantum interferometric approach. The proposed quantum sensor consists of many surface-state electrons trapped individually on liquid helium by an electrode-network at the bottom of the liquid helium film.
This paper applies results on the robust stability of nonlinear quantum systems to a system consisting an optical cavity containing a saturated Kerr medium. The system is characterized by a Hamiltonian operator which contains a non-quadratic term involving a quartic function of the annihilation and creation operators....
The revival structure of wave packets is examined for quantum systems having energies that depend on two nondegenerate quantum numbers. For such systems, the evolution of the wave packet is controlled by two classical periods and three revival times.
I consider a spin chain with nearest-neighbor and next nearest-neighbor interactions. I show that the Hamiltonian obtained by specifying the desired combination of symmetry blocks is a fast scrambler.
We strengthen the connection between Information Theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization procedure results in a decomposition of the quantum kinetic energy as the sum of a cl...
Recent investigations suggest that the discrete linear unitary group $U(N)$ can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical justifications, no formal proof has been provided.
A quantum system subjected to a strong continuous monitoring undergoes quantum jumps. This very well known fact hides a neglected subtlety: sharp scale-invariant fluctuations invariably decorate the jump process even in the limit where the measurement rate is very large.
Matrix permanents are hard to compute or even estimate in general. It had been previously suggested that the permanents of Positive Semidefinite (PSD) matrices may have efficient approximations.
We propose a scheme to implement a heralded quantum memory for single-photon polarization qubits with a single atom trapped in an optical cavity. In this scheme, an injected photon only exchanges quantum state with the atom, so that the heralded storage can be achieved by detecting the output photon.
Great progress has been made recently in establishing conditions for separability of a particular class of Werner densities on the tensor product space of $n$ $d$--level systems (qudits). In this brief note we complete the process of establishing necessary and sufficient conditions for separability of these Werner den...
Bifractional displacement operators, are introduced by performing two fractional Fourier transforms on displacement operators. They are shown to be special cases of elements of the group G, that contains both displacements and squeezing transformations.
Magnons can endow quantum devices with new functionalities. Assessing their potential requires precise characterization of magnon properties.
We show that the sensitivity of an atomic clock can be enhanced below the shot-noise level by initially squeezing, and then measuring in output, the population of a single atomic level. This can simplify current experimental protocols which requires squeezing of the relative number of particles of the two populated st...
We derive the general formula giving the Berry phase for an arbitrary spin, having both magnetic-dipole and electric-quadrupole couplings with external time-dependent fields. We assume that the effective E and B fields remain orthogonal during the quantum cycles.
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics.
The most important ability of a quantum channel is to preserve the quantum properties of transmitted quantum states. We experimentally demonstrate a continuous-variable system for efficient benchmarking of quantum channels.
We propose a phenomenological Hamiltonian for the interaction of neutral macroscopic bodies with the electromagnetic field. Subsequently we revisit the assumption according to which the retarded interactions between neutral macroscopic bodies can be obtained through an additive principle i.e. summing the volume elemen...
Monitoring the fluorescent radiation of an atom unravels the master equation evolution by collapsing the atomic state into a pure state which evolves stochastically. A robust unraveling is one that gives pure states that, on average, are relatively unaffected by the master equation evolution (which applies once the mo...
The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state $\psi_I$ may need so as to evolve into a state orthogonal to itself. Recently [V.
Complete characterization of complete positivity preserving non-Markovian master equations is presented.
Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible.
Twin-field quantum key distribution (TFQKD), using single-photon-type interference, offers a way to exceed the rate-distance limit without quantum repeaters. However, it still suffers from the photon losses and dark counts, which impose an ultimate limit on its transmission distance.
Recently it was demonstrated that long-lived quantum coherence exists during excitation energy transport in photosynthesis. It is a valid question up to which length, time and mass scales quantum coherence may extend, how to one may detect this coherence and what if any role it plays for the dynamics of the system.
We demonstrate real-time magnetometry by detecting fluorescence from a nitrogen vacancy center in the setting of coherent population trapping and by estimating magnetic field from the time series of the observed photon counts, which are correlated with the underlying field. The proof-of-principle experiment uses an ex...
We study the properties of classical and quantum stable structures in a 3D parameter space corresponding to the dissipative kicked top. This is a model system in quantum and classical chaos that gives a starting point for many body examples.
A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally.
Dispersive interactions of matter qubits with bright squeezed light in a high-Q cavity is studied. Numerical simulation shows that higher fidelity of operations to obtain a certain phase shift of the pulse through the dispersive light-matter interaction may be reached using bright squeezed light than that using bright...
Atoms and ions confined with electric and optical fields form the basis of many current quantum simulation and computing platforms. When excited to high-lying Rydberg states, long-ranged dipole interactions emerge which strongly couple the electronic and vibrational degrees of freedom through state-dependent forces.
We numerically and experimentally show that all photons generated by spontaneous parametric down-conversion (SPDC) follow a transverse amplitude similar to that of the pump. This amplitude transfer from pump to SPDC is revealed in the Fourier image plane of the down-converted photons restricted by an aperture.
We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state $\sigma$.
In this work we proof that boson sampling with $N$ particles in $M$ modes is equivalent to short-time evolution with $N$ excitations in an XY model of $2N$ spins. This mapping is efficient whenever the boson bunching probability is small, and errors can be efficiently postselected.
A useful approach is investigated in order to analyze a class of a stochastic differential equations that can be encountered in quantum optics problems, especially, in the case of two photon losses on the driven cavity mode. The passage to the ordinary coupled differential equations is presented and the treatment of t...
The computation of electronic structure properties at the quantum level is a crucial aspect of modern physics research. However, conventional methods can be computationally demanding for larger, more complex systems.
We propose a gradient-based general computational framework for optimizing model-dependent parameters in quantum batteries (QB). We apply this method to two different charging scenarios in the micromaser QB and we discover a charging protocol for stabilizing the battery in upper-laying Hilbert space chambers in a cont...
This work explores Boltzmann's time hypothesis, which associates the perceived direction of "time flow" with the second law of thermodynamics. We discuss mechanisms that can be responsible for the action of the second law, for directional properties of time and, ultimately, for the perception that past eve...
We review the unconventional photon blockade mechanism. This quantum effect remarkably enables a strongly sub-Poissonian light statistics, even from a system characterized by a weak single photon nonlinearity.
We show that by switching on a spin-orbit interaction in a cold-atom system, experiencing a Zeeman-like coupling to an external field, e.g., in a Bose-Einstein condensate, one can simulate a quantum measurement on a precessing spin. Depending on the realization, the measurement can access both the ergodic and the Zeno...
Atoms coupled to nanophotonic interfaces represent an exciting frontier for the investigation of quantum light-matter interactions. While most work has considered the interaction between statically positioned atoms and light, here we demonstrate that a wealth of phenomena can arise from the self-consistent interaction...
We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five and seven-qubit stabilizer codes.
We generalize the universally composable definition of Canetti to the Quantum World. The basic idea is the same as in the classical world.
We disclose the behaviour of quantum and classical correlations among all the different spatial-temporal regions of a space-time with an event horizon, comparing fermionic with bosonic fields. We show the emergence of conservation laws for entanglement and classical correlations, pointing out the crucial role that sta...
We develop a flow renormalization approach for periodically-driven quantum systems, which reveals prethermal dynamical regimes and associated timescales via direct correspondence between real time and flow time behavior. In this formalism, the dynamical problem is recast in terms of coupling constants of the theory fl...
We construct a new error-suppression scheme that makes use of the adjoint of reversible quantum algorithms. For decoherence induced errors such as depolarization, it is presented that provided the depolarization error probability is less than 1, our scheme can exponentially reduce the final output error rate to zero u...
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.
The accurate (or even approximate) solution of the equations that govern the dynamics of dissipative quantum systems remains a challenging task for quantum science. While several algorithms have been designed to solve those equations with different degrees of flexibility, they rely mainly on highly expensive iterative...
We present a formalism for encoding the logical basis of a qubit into subspaces of multiple physical levels. The need for this multilevel encoding arises naturally in situations where the speed of quantum operations exceeds the limits imposed by the addressability of individual energy levels of the qubit physical syst...
Ground-state cooling is essential for accessing the quantum regime and enabling quantum control of macroscopic systems. However, achieving optomechanical cooling in the unresolved-sideband regime ($\omega_b < \kappa$) remains challenging.
We present a proof-of-concept experiment aimed at increasing the sensitivity of temperature sensors implemented with Fiber Bragg gratings by making use of a weak value amplification scheme. The technique requires only linear optics elements for its implementation, and appears as a promising method for extending the ra...
The two-photon Rabi Hamiltonian is a simple model describing the interaction of light with matter, with the interaction being mediated by the exchange of two photons. Although this model is exactly soluble in the rotating-wave approximation, we work with the full Hamiltonian, maintaining the non-integrability of the m...
We show that radiation damage to unstained biological specimens is not an intractable problem in electron microscopy. When a structural hypothesis of a specimen is available, quantum mechanical principles allow us to verify the hypothesis with a very low electron dose.
Quantum mechanical effects induced by the miniaturization of complementary metal-oxide-semiconductor (CMOS) technology hamper the performance and scalability prospects of field-effect transistors. However, those quantum effects, such as tunnelling and coherence, can be harnessed to use existing CMOS technology for qua...
The dynamics of single electron and nuclear spins in a diamond lattice with different 13C nuclear spin concentration is investigated. It is shown that coherent control of up to three individual nuclei in a dense nuclear spin cluster is feasible.
Quantum entanglement systems based on qudits dilate high-dimensional (HD) state spaces and enhance resistance to loss in quantum information processing (QIP). To fully exploit this potential, effective schemes for generating HD entanglement are crucial.
We predict that the phase-dependent error distribution of locally unentangled quantum states directly affects quantum parameter estimation accuracy. Therefore, we employ the displaced squeezed vacuum (DSV) state as a probe state and investigate an interesting question of the phase-sensitive nonclassical properties in ...
In this work, we propose a novel architecture (and several variants thereof) based on quantum cryptographic primitives with provable privacy and security guarantees regarding membership inference attacks on generative models. Our architecture can be used on top of any existing classical or quantum generative models.
We introduce an exact mapping between the Dirac equation in (1+1)-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1+1)-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac part...
We investigate the effectiveness of different dynamical decoupling protocols for storage of a single qubit in the presence of a purely dephasing bosonic bath, with emphasis on comparing quantum coherence preservation under uniform vs. non-uniform delay times between pulses. In the limit of instantaneous bit-flip pulse...
By the time of writing, quantum audio still is a very young area of study, even within the quantum signal processing community. This chapter introduces the state of the art in quantum audio and discusses methods for the quantum representation of audio signals.
A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action.
We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case.
Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit).
Negatively charged group-IV defects in diamond show great potential as quantum network nodes due to their efficient spin-photon interface. However, reaching sufficiently long coherence times remains a challenge.
In this Letter we give a method for constructing sets of simple circuits that can determine the spectrum of a partially transposed density matrix, without requiring either a tomographically complete POVM or the addition of noise to make the spectrum non-negative. These circuits depend only on the dimension of the Hilb...
Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminates topological entanglement entropy.
We give a tight scheme for teleporting a quantum state between two parties whose reference frames are misaligned by an action of a finite symmetry group. Unlike previously proposed schemes, ours requires no additional tokens or data to be passed between the participants; the same amount of classical information is tra...
We present a study of the achievable rates for classical information transmission via a lossy bosonic channel with memory, using homodyne detection. A comparison with the memoryless case shows that the presence of memory enhances the bit rate if information is encoded in collective states, i.e. states which are entang...
The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert-Schmidt and Bures-Hall ensembles.
The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directl...
We consider the problem of minimum-error quantum state discrimination for single-qubit mixed states. We present a method which uses the Helstrom conditions constructively and analytically; this algebraic approach is complementary to existing geometric methods, and solves the problem for any number of arbitrary signal ...
We study the behaviour of two different measures of the complexity of multipartite correlation patterns, weaving and neural complexity, for symmetric quantum states. Weaving is the weighted sum of genuine multipartite correlations of any order, where the weights are proportional to the correlation order.
We investigate gap-closings in one- and two-dimensional tight-binding models with two bands, containing non-Hermitian hopping terms, and open boundary conditions (OBCs) imposed along one direction. We compare the bulk OBC spectra with the periodic boundary condition (PBC) spectra, pointing out that they do not coincid...
Quantum sensors have attracted broad interest in the quest towards sub-micronscale NMR spectroscopy. Such sensors predominantly operate at low magnetic fields.
Quantum backaction disturbs the measurement of the position of a mechanical oscillator by introducing additional fluctuations. In a quantum backaction measurement technique, the backaction can be evaded, although at the cost of losing part of the information.
We prove that it is impossible to construct perfect-complete quantum public-key encryption (QPKE) with classical keys from quantumly secure one-way functions (OWFs) in a black-box manner, resolving a long-standing open question in quantum cryptography. Specifically, in the quantum random oracle model (QROM), no perfec...
We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a Lévy Stable (fat-tailed) distribution. Lévy random matrices are known to demonstrate non-ergodic behaviour through the emergence of a mobility edge.
Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and thus places an annealing rate bottleneck for high success probability.
The work deficit, as introduced by Jonathan Oppenheim \emph{et al}[Phys. Rev. Lett.
Sensing and measurement tasks in severely adverse conditions such as loss, noise and dephasing can be improved by illumination with quantum states of light. Previous results have shown a modest reduction in the number of measurements necessary to achieve a given precision.
An author (<a href="https://arxiv.org/abs/1709.09262" data-arxiv-id="1709.09262" class="link-https">arXiv:1709.09262</a> [quant-ph] (2017), Nanoscale Research Letters (2017) 12:552) has recently questioned the security of two-way quantum key distribution schemes by referring to attack strategies which leave no errors i...
The spin-wave (SW) NOON state is an $N$-particle Fock state with two atomic spin-wave modes maximally entangled. Attributed to the property that the phase is sensitive to collective atomic motion, the SW NOON state can be utilized as a novel atomic interferometer and has promising application in quantum enhanced measu...
Recently, the bound state solutions of a confined Klein-Gordon particle under the mixed scalar-vector generalized symmetric Woods-Saxon potential in one spatial dimension have been investigated. The obtained results reveal that in the spin symmetric limit discrete spectrum exists, while in the pseudo-spin symmetric li...
We introduce a novel technique for efficiently cooling many-body quantum systems with unknown Hamiltonians down to their ground states with a high fidelity. The technique involves initially applying a strong external field followed by a sequence of single-degree-of-freedom (single-qubit) measurements and radiofrequenc...
A new database of collisional rate coefficients for transitions between the rotational states of H$_2$O collided with H$_2$ background gas is developed. The goal is to expand over the other existing databases in terms of the rotational states of water (200 states are included here) and the rotational states of hydroge...

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