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Upper bounds for private communication over quantum channels can be derived by adopting channel simulation, protocol stretching, and relative entropy of entanglement. All these ingredients have led to single-letter upper bounds to the secret key capacity which can be directly computed over suitable resource states.
The Fock space of a system of indistinguishable particles is isomorphic (in a non-unique way) to the state-space of a composite i.e., many-modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic systems.
Resource theory is a widely-applicable framework for analyzing the physical resources required for given tasks, such as computation, communication, and energy extraction. In this paper, we propose a general scheme for analyzing resource theories based on resource destroying maps, which leave resource-free states uncha...
We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any classical-quantum feedback loop, bypass the barren plateau problem and does not nece...
Quantum mechanics allows processes to be superposed, leading to a genuinely quantum lack of causal structure. For example, the process known as the quantum switch applies two operations ${\cal A}$ and ${\cal B}$ in a superposition of the two possible orders, ${\cal A}$ before ${\cal B}$ and ${\cal B}$ before ${\cal A}...
The protocols for controlled remote state preparation of a single qubit and a general two-qubit state are presented in this paper. The general pure three-qubit states are chosen as shared quantum channel, which are not LOCC equivalent to the mostly used GHZ-state.
The spontaneous switching of a quantum particle between the wells of a double-well potential is a phenomenon of general interest to physics and chemistry. It was broadly believed that the switching rate decreases steadily with the size of the energy barrier.
We show that when the proper description of the behaviour of individual photons or spin 1/2 particles in a spherically symmetric entangled pair is done through the use of the density matrix, the Leggett's inequality is not violated by quantum mechanics.
We study the adiabatic evolution of a two-level model in the presence of an external classical electric field. The coupling between the quantum model and the classical field is taken in the electric dipole approximation.
We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalisation of Mealy machines.
The NewtonWigner basis of orthonormal localized states is generalized to orthonormal and relativistic biorthonormal bases on an arbitrary hyperplane in spacetime. This covariant formalism is applied to the measurement of photon location using a hypothetical 3D array with pixels throughout space turned on at a fixed ti...
A key element in the study of cold atoms, and their use in emerging quantum technologies, is trapping the atoms in an ultra-high vacuum (UHV) chamber. Many methods have been used to trap atoms including atom chips and magneto-optical traps (MOTs).
We find a new highly symmetrical and very numerous class (millions of non-isomorphic sets) of 4-dim Kochen-Specker (KS) vector sets. Due to the nature of their geometrical symmetries, they cannot be obtained from previously known ones.
A proposal is put forward for an estimate of the duration of a transition between atomic states. The proposal rests on the consideration that a resonance of the atomic electron with modes of the zero-point radiation field of Compton's frequency is at the core of the phenomenon.
We study the equilibrium and non-equilibrium physics of two qubits interacting through an ultrastrong coupled qubit-cavity system. By tuning the qubits energy gap while keeping the ultrastrong coupling system to its ground state, we demonstrate a strong two-qubit interaction as well as an enhanced excitation transfer ...
The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics.
The algebraic approach to operator perturbation method has been applied to two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator'' and ``The Generalized Zeeman Effect''. To that end, two realizations of the superoperators involved in the formalism have been carried out. The first...
Quantum sensing is highly attractive for accessing spectral regions in which the detection of photons is technically challenging: sample information is gained in the spectral region of interest and transferred via entanglement into another spectral range, for which highly sensitive detectors are available. This is esp...
In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard-tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial ...
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent to a boundary.
Keeping in view the exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that Ising type Hamiltonian does not retain the exchange symmetry of initially symmetric multiqubit states. Specifically, we show that all N-qubit states (N greater than or equal to 5) obeying permutation symmetry ...
Pilot wave theory endows particles with definite positions at all times governed by deterministic dynamics. However, individual particle trajectories are generically undetectable by experiment.
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over the corresponding classical algorithms.
Superconducting cavities have emerged as a key tool for measuring the spin states of quantum dots. So far however, few experiments have explored longitudinal couplings between dots and cavities, and no solid-state qubit experiments have explicitly probed the "adiabatic" regime, where the Purcell decay is stron...
Constructing quantum circuits for efficient state preparation belongs to the central topics in the field of quantum information and computation. As the number of qubits grows fast, methods to derive large-scale quantum circuits are strongly desired.
The Orthodox kinetic energy has, in fact, two hidden-variable components: one linked to the current (or Bohmian) velocity, and another linked to the osmotic velocity (or quantum potential), and which are respectively identified with phase and amplitude of the wavefunction. Inspired by Bohmian and Stochastic quantum me...
We investigate the consequences of introducing non-uniform initial conditions in the dynamics of spin ensembles characterized by all-to-all interactions. Specifically, our study involves the preparation of a set of semi-classical spin ensembles with varying orientations.
We consider the problem of $\textit{subgroup testing}$ for a quantum circuit $C$: given access to $C$, determine whether it implements a unitary that is $a$-close or $b$-far from a subgroup $\mathcal{G}$ of the unitary group. It encompasses the problem of exact testing, property testing and tolerant testing.
Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and a well-defined experimental procedure for estimating the distinguishability mea...
We present the theoretical basis for and experimental verification of arbitrary single-qubit state generation, using the polarization of photons generated via spontaneous parametric downconversion. Our precision measurement and state reconstruction system has the capability to distinguish over 3 million states, all of...
This work summarizes the most important developments in the construction and application of the Dirac-Moshinsky oscillator (DMO) with which the author has come in contact. The literature on the subject is voluminous, mostly because of the avenues that exact solvability opens towards our understanding of relativistic q...
In this work, the non-relativistic wave equation via the Schrödinger wave equation under the influence of the Aharonov-Bohm flux field Subject to physical potentials of various kinds is investigated. These potentials are modified Coulomb potential, modified harmonic oscillator potential, the Kratzer-Feus potential, an...
Quasiprobabilistic decompositions (QPDs) play a key role in maximizing the utility of near-term quantum hardware. For example, Probabilistic Error Cancellation (PEC) (an error mitigation technique) and circuit cutting (which enables large quantum computations to be performed on quantum hardware with a limited number o...
We suggest a quantum measurement model in an ion trap which specifies the probability distribution of two, distinct internal ground states of a trapped four-level ion. The external degrees of motion of the four-level ion constitute the meter which, in turn, is coupled to the environment by engineered reservoirs.
We propose a variational approach for preparing entangled quantum states on quantum computers. The methodology involves training a unitary operation to match with a target unitary using the Fubini-Study distance as a cost function.
This doctoral dissertation presents an in-depth analysis of the first six chapters of Eddington's Fundamental Theory, sometimes referred to as his 'statistical' theory, in the context of discoveries and advancements made since its original publication in 1946. In particular, the analysis is focused on bein...
The textbook effective-range expansion of scattering theory is useful in the analysis of low-energy scattering phenomenology when the scattering length $\|a\|$ is much larger than the range $R$ of the scattering potential: $\|a\|\gg R$. Nevertheless, the same has been used for systems where the scattering length is much s...
Recent developments in quantum technology mean that is it now possible to manipulate systems and measure fermion fields (e.g. reservoirs of electrons) at the quantum level. This progress has motivated some recent work on filtering theory for quantum systems driven by fermion fields by Korotkov, Milburn and others.
Noise in optical Telecom fibers is an important limitation on optical quantum data transmission. Unfortunately, the classically successful amplifiers (such as EDFA) cannot be used in quantum communication because of the no-cloning theorem.
We theoretically investigate the mechanical effect of the light-induced dipole-dipole interaction potential on the atoms in a Bose-Einstein condensate. We present numerical calculations on the magnitude and shape of the induced potentials for different experimentally accessible geometries.
Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts of this entropy and other related definitions can be applied to the study of qu...
A new approach to precise determination of atomic matrix elements is described whereby measurement of spectral locations of zeros in the Rayleigh scattering cross-section allows frequency-domain extraction of matrix elements in terms of a fiducial quantity. Illustrations are made for scattering off the ground state in...
We propose a quantum unstructured search algorithm to find the extrema or roots of discrete functions, $f(\mathbf{x})$, such as the objective functions in combinatorial and other discrete optimisation problems. The first step of the Quantum Search for Extrema and Roots Algorithm (QSERA) is to translate conditions of t...
The dynamics of a kicked quantum system undergoing repeated measurements of momentum is investigated. A diffusive behavior is obtained even when the dynamics of the classical counterpart is not chaotic.
An accelerating photodetector is predicted to see photons in the electromagnetic vacuum. However, the extreme accelerations required have prevented the direct experimental verification of this quantum vacuum effect.
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a single phase, applications to the simultaneous estimation of several phases ma...
Quantum mechanics is nonlocal. Classical mechanics is local.
We study the speed/fidelity trade-off for a two-qubit phase gate implemented in $^{43}$Ca$^+$ hyperfine trapped-ion qubits. We characterize various error sources contributing to the measured fidelity, allowing us to account for errors due to single-qubit state preparation, rotation and measurement (each at the $\sim0....
This paper is a comparison of two theories of the probability of a history in quantum mechanics. One is derived from Copenhagen quantum mechanics using the projection postulate and is the basis of the "consistent histories" interpretation; the other is based on a proposal by Bell, originally for the "pilot...
The using of quantum parallelism is often connected with consideration of quantum system with huge dimension of space of states. The n-qubit register can be described by complex vector with 2^n components (it belongs to n'th tensor power of qubit spaces).
Long-distance quantum communication and networking require quantum memory nodes with efficient optical interfaces and long memory times. We report the realization of an integrated two-qubit network node based on silicon-vacancy centers (SiVs) in diamond nanophotonic cavities.
The contribution of different modes of the Coulomb field to decoherence and to the dynamical breakdown of the time reversal invariance is calculated in the one-loop approximation for non-relativistic electron gas. The dominant contribution was found to come from the usual collective modes in the plasma, namely the zer...
The Quantum Alternating Operator Ansatz (QAOA) represents a branch of quantum algorithms for solving combinatorial optimization problems. A specific variant, the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA), ensures uniform amplitude across states that share equivalent objective values.
One of the remarkable features of quantum mechanics is the ability to ensure secrecy. Private states embody this effect, as they are precisely those multipartite quantum states from which two parties can produce a shared secret that cannot in any circumstance be correlated to an external system.
In this paper, we investigate how the evolution of the states of two qubits initially in a direct product state can be controlled by the optical field in a Tavis-Cummings (TC) model. For the two qubits initially in the direct product state, we find that their matrix elements at any moment can be modulated by the coeff...
Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation.
Hybrid quantum systems involving solid-state spins and superconducting microwave cavities play a crucial role in quantum science and technology, but improving the spin-photon coupling at the single quantum level remains challenging in such systems. Here, we propose a simple technique to strongly couple a single solid-...
The spin resonance of electrons can be coupled to a microwave cavity mode to obtain a photon-magnon hybrid system. These quantum systems are widely studied for both fundamental physics and technological quantum applications.
The displacement of micro-electro-mechanical-systems (MEMS) cantilevers is used to measure a broad variety of phenomena in devices ranging from force microscopes to biochemical sensors to thermal imaging systems. We demonstrate the first direct measurement of a MEMS cantilever displacement with a noise floor at 40% of...
This document is a pdf version of the series of blogposts about variational quantum algorithms (VQA) I originally posted on my blog Musty Thoughts. It provides an explanation of the basic variational algorithms, such as Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA), as wel...
Loop-based boson samplers interfere photons in the time degree of freedom using a sequence of delay lines. Since they require few hardware components while also allowing for long-range entanglement, they are strong candidates for demonstrating quantum advantage beyond the reach of classical emulation.
This paper elucidates the dual structure of the Schrödinger dynamics in two correlated stages: (1) We first derive the real-valued Schrödinger equation from scratch without referring to classical mechanics, wave mechanics, nor optics, and thereby attain a concrete and clear interpretation of the Schrödinger (wave) func...
We report on our progress developing highly-miniaturised, polarisation-entangled, photon pair sources for CubeSats. We have a correlated photon-pair source in orbit in the NUS Galassia 2U CubeSat.
As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum likelihood, least squares, generalised least squares, positive least squares, ...
Relaxation rates provide important characteristics both for classical and quantum processes. Essentially they control how fast the system thermalizes, equilibrates, {decoheres, and/or dissipates}.
Cavity-QED is a promising avenue for the deterministic generation of entangled and spin-squeezed states for quantum metrology. One archetypal scheme generates squeezing via collective one-axis twisting interactions.
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with membership queries under the uniform distribution with error $1/2 - \gamma$ by a ...
We investigate the evolution of entanglement in multiple-quantum (MQ) NMR experiments in crystals with pairs of close nuclear spins-1/2. The initial thermodynamic equilibrium state of the system in a strong external magnetic field evolves under the non-secular part of the dipolar Hamiltonian.
Control of multi-level quantum systems is sensitive to implementation errors in the control field and uncertainties associated with system Hamiltonian parameters. A small variation in the control field spectrum or the system Hamiltonian can cause an otherwise optimal field to deviate from controlling desired quantum s...
A relevant problem in the theory of open quantum systems is the lack of complete positivity of dynamical maps obtained after weak-coupling approximations, a famous example being the Redfield master equation. A number of approaches exist to recover well-defined evolutions under additional Markovian assumptions, but muc...
We study the nature of the ergodicity-breaking "quantum many-body scar" states that appear in the PXP model describing constrained Rabi oscillations. For a {wide class of bipartite lattices} of Rydberg atoms, we reveal that the nearly energy-equidistant tower of these states arises from the Hamiltonian's c...
It is well known that non-Hermitian systems can be extremely sensitive to boundary conditions owing to non-Hermitian skin effect (NHSE). Analogously, we investigate two boundary-sensitive $U(1)$ symmetric Lindbladians: one carries current in the steady state, and the other does not.
In the last decade, there has been remarkable progress on the practical integration of on-chip quantum photonic devices yet quantum state generators remain an outstanding challenge. Simultaneously, the quantum-dot photonic-crystal-resonator platform has demonstrated a versatility for creating nonclassical light with t...
We propose two experimental schemes for quantum state discrimination that achieve the optimal tradeoff between the probability of correct identification and the disturbance on the quantum state.
The SSSV model is a simple classical model that achieves excellent correlation with published experimental data on the D-Wave machine's behavior on random instances of its native problem, thus raising questions about how "quantum" the D-Wave machine is at large scales. In response, a recent preprint by Vin...
Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian.
In this work, we explore the notions unextendible product basis and uncompletability for operators which remain positive under partial transpose. Then, we analyze their connections to the ensembles which are many-copy indistinguishable under local operations and classical communication (LOCC).
In spite of many attempts, no local realistic model seems to be able to reproduce EPR-Bell type correlations, unless non ideal detection is allowed. The low efficiency of detectors in all experiments with photons makes the use of the fair sampling assumption unavoidable.
Quantum Ising model in a transverse field is of the simplest quantum many body systems used for studying universal properties of quantum phase transitions. Interestingly, it is well-known that such phase transitions can be mapped to topological phase transitions in Toric code models.
Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group of the surface complex.
Calculating the observable properties of chemical systems is often classically intractable and is widely viewed as a promising application of quantum information processing. Yet one of the most common and important chemical systems in nature - the hydrogen bond - has remained a challenge to study using quantum hardwar...
The entanglement and quantum correlation measures have been investigated for the ground state of a spin chain with a Kitaev-type exchange interactions on alternating bonds, along with a transverse magnetic field. There is a macroscopic degeneracy in the ground state for zero magnetic field, implying a quantum critical...
The impressive pace of advance of quantum technology calls for robust and scalable techniques for the characterization and validation of quantum hardware. Quantum process tomography, the reconstruction of an unknown quantum channel from measurement data, remains the quintessential primitive to completely characterize ...
Designing effective quantum models for real-world tasks remains a key challenge within Quantum Machine Learning (QML), particularly in applications such as credit card fraud detection, where extreme class imbalance and evolving attack patterns demand both accuracy and adaptability. Most existing approaches rely on eit...
We study what is arguably the most experimentally appealing Boson Sampling architecture: Gaussian states sampled with threshold detectors. We show that in this setting, the probability of observing a given outcome is related to a matrix function that we name the Torontonian, which plays an analogous role to the perman...
The entanglement content of high-dimensional random pure states is almost maximal, nevertheless, we show that, due to the complexity of such states, the detection of their entanglement using witness operators is rather difficult. We discuss the case of unknown random states, and the case of known random states for whi...
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties.
To coherently control a few-level quantum emitter, typically pulses with an energy resonant to the transition energy are applied making use of the Rabi mechanism, while a single off-resonant pulse does not result in a population inversion. Surprisingly, a two-color excitation with a combination of two off-resonant pul...
Spontaneous Parametric Down-Conversion (SPDC), also known as parametric fluorescence, parametric noise, parametric scattering and all various combinations of the abbreviation SPDC, is a non-linear optical process where a photon spontaneously splits into two other photons of lower energies. One would think that this ar...
We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition ba...
High pressure experiments in diamond anvil cells as well as in geophysics show that at certain discrete values of pressure abrupt changes of the mass density and changes of the material structure occur. The aim of this paper is to discuss the influence of high external pressure on atoms and molecules using the $3D$ sq...
A three-state system subjected to a time-dependent Hamiltonian whose bare energies undergo one or more crossings, depending on the relevant parameters, is considered, also taking into account the role of dissipation in the adiabatic following of the Hamiltonian eigenstates. Depending on the fact that the bare energies...
Quantum mechanics forbids perfect discrimination among nonorthogonal states through a single shot measurement. To optimize this task, many strategies were devised that later became fundamental tools for quantum information processing.
In this work I demonstrate the interference of three photons, a generalisation of the famous Hong Ou Mandel (HOM) interference. I show that three-photon interference is governed by four parameters and measure three-photon interference independent of two-photon interference.
Kerr-cat qubits have been experimentally shown to exhibit a large noise bias, with one decay channel suppressed by several orders of magnitude. In superconducting implementations, increasing the microwave drive on the nonlinear oscillator that hosts the Kerr-cat qubit should, in principle, further enhance this bias.
Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases.
The impossibility proof on unconditionally secure quantum bit commitment is critically reviewed. Different ways of obtaining secure protocols are indicated.
We examine the perfect cloning of non-local, orthogonal states with only local operations and classical communication. We provide a complete characterisation of the states that can be cloned under these restrictions, and their relation to distinguishability.
We propose a method to mitigate measurement errors in the distribution counts of a Quantum computer using image contrast filters. This work is similar to the method described by Gambetta and colleagues in [1]; however our technique does not use a linear system of equations, but an image contrast filter to mitigate the...
The rapid progress in the development of quantum devices is in large part due to the availability of a wide range of characterization techniques allowing to probe, test and adjust them. Nevertheless, these methods often make use of approximations that hold in rather simplistic circumstances.

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