arXiv subjects

V. S. Shchesnovich

Publications and source records attributed to V. S. Shchesnovich.

At least 19 recordsLinked to original sources

arXiv2026

The second quantization method for indistinguishable particles (Lecture Notes in Physics, UFABC 2010)

Summary of the lectures: 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of indistinguishable particles 1.3 Definition and properties of the creation and annihilation operators 1.4 TheFockspace 1.5 The representations of state vectors and operators 1.5.1 N-particlewave-functions 1.5.2 The second-quantization representation of operators 1.5.3 Examples 1.6 Evolution of operators in the Heisenberg picture 1.7 Statistical operators of indistinguishable particles 1.7.1 The averages of the s-particle operators 1.7.2 The general structure of the one-particle statistical operator 2 Quadratic Hamiltonian and the diagonalization 2.1 Diagionalization of the Hamiltonian quadratic in the fermion operators 2.2 Diagionalization of the Hamiltonian quadratic in the boson operators 2.2.1 Diagonalization of the quadratic bosonic Hamiltonian possessing a zero mode 2.3 Long range order, condensation and the Bogoliubov spectrum of weakly interacting Bose gas 2.3.1 The excitation spectrum of weakly interacting Bose gas inabox 2.3.2 The excitation spectrum of an interacting Bose gas in an externalpotential 2.4 The Jordan-Wigner transformation: fermionization of interacting 1D spin chains

cond-mat.quant-gas↗

arXiv2025

Isoenergetic model for optical downconversion and error-specific limits of the parametric approximation

Optical downconversion is widely used for generating photon pairs, squeezed and entangled states of light, making it an indispensable tool in quantum optics and quantum information. In the regime where the pump is much stronger than the generated field, the standard parametric approximation treats the pump amplitude as a fixed parameter of the model. This approximation has a limited domain of validity since it assumes a non-depleted and non-entangled pump. By finding an approximate solution to the Schrödinger equation of the downconversion process, we obtain an improved analytical model beyond the parametric one, which accounts for pump depletion and pump-signal entanglement. The new model is advantageous, first, because it allows one to compute averages of field operators far beyond the domain of validity of the parametric approximation, and second, because it allows one to establish error-specific limits of the latter domain. For a given pump amplitude, we find a maximum squeezing parameter, up to which the approximation remains valid within a specified acceptable error. Our results confirm that recent experiments on Gaussian boson sampling, with a squeezing parameter of $r\approx 1.8$ and a coherent pump amplitude of $α\approx 2\cdot10^6$, can still be accurately described by the standard parametric approximation. However, we observe a sharp decline in validity as the squeezing parameter increases. For pump amplitudes of $α\approx 2\cdot10^6$, the parametric approximation breaks down when the squeezing parameter exceeds $r\approx 4.5$, whereas the new approximation remains valid up to $r\approx 6$ with an acceptable error of 1%.

quant-ph↗

arXiv2020

Distinguishability theory for time-resolved photodetection and boson sampling

We study distinguishability of photons in multiphoton interference on a multiport when fast detectors, capable of precise time resolution, are employed. Such a setup was previously suggested for experimental realization of boson sampling with single photons. We investigate if fast photodetection allows to circumvent distinguishability of realistic single photons in mixed states. To this goal we compare distinguishability of photons in two setups: (a) with photons in the same average (temporal) profile on a spatial interferometer and photodetection incapable of (or with strongly imprecise) time resolution and (b) with photons in generally different average temporal profiles on the same spatial interferometer and photodetection with precise time resolution. Exact analytical results are obtained for Gaussian-shaped single photons with Gaussian distribution of photon arrival time. Distinguishability of photons in the two setups is found to be strikingly similar. For the same purity of photon states, only the same quality experimental boson sampling can be achieved using either of the two setups. The upshot of our results is that distinguishability due to mixed states is an intrinsic property of photons, whatever the photodetection scheme.

quant-ph↗

arXiv2018

Collective phases of identical particles interfering on linear multiports

We introduce collective geometric phases of bosons and fermions interfering on a linear unitary multiport, where each phase depends on the internal states of identical particles (i.e., not affected by the multiport) and corresponds to a cycle of the symmetric group. We show that quantum interference of $N$ particles in generic pure internal states, i.e., with no pair being orthogonal, is governed by $(N-1)(N-2)/2$ independent triad phases (each involving only three particles). The deterministic distinguishability, preventing quantum interference with two or three particles, allows for the genuine $(N\ge 4)$-particle phase (interference) on a multiport: setting each particle to be deterministically distinguishable from all others except two by their internal states allows for a novel (circle-dance) interference of $N\ge 4$ particles governed by a collective $N$-particle phase, while simultaneously preventing the $R$-particle interference for $3\le R\le N-1$. The genuine $N$-particle interference manifests the $N$th order quantum correlations between identical particles at a multiport output, it does not appear in the marginal probability for a subset of the particles, e.g., it cannot be detected if at least one of the particles is lost. This means that the collective phases are not detectable by the usual "quantumness" criteria based on the second-order quantum correlations. The results can be useful for quantum computation, quantum information, and other quantum technologies with single photons. \end{abstract}

quant-ph↗

arXiv2017

Quantum De Moivre-Laplace theorem for noninteracting indistinguishable particles

The asymptotic form of the average probability to count $N$ indistinguishable identical particles in a small number $r \ll N$ of binned-together output ports of a $M$-port Haar-random unitary network, proposed recently in \textit{Scientific Reports} \textbf{7}, 31 (2017) in a heuristic manner with some numerical confirmation, is presented with the mathematical rigor and generalized to an arbitrary (mixed) input state of $N$ indistinguishable particles. It is shown that, both in the classical (distinguishable particles) and quantum (indistinguishable particles) cases, the average counting probability into $r$ output bins factorizes into a product of $r-1$ counting probabilities into two bins. This fact relates the asymptotic Gaussian law to the de Moivre-Laplace theorem in the classical case and similarly in the quantum case where an analogous theorem can be stated. The results have applications to the setups where randomness plays a key role, such as the multiphoton propagation in disordered media and the scattershot Boson Sampling.

quant-ph↗

arXiv2016

Universality of Generalized Bunching and Efficient Assessment of Boson Sampling

It is found that identical bosons (fermions) show generalized bunching (antibunching) property in linear networks: The absolute maximum (minimum) of probability that all $N$ input particles are detected in a subset of $\mathcal{K}$ output modes of any nontrivial linear $M$-mode network is attained \textit{only} by completely indistinguishable bosons (fermions). For fermions $\mathcal{K}$ is arbitrary, for bosons it is either ($i$) arbitrary for only classically correlated bosons or ($ii$) satisfies $\mathcal{K}\ge N$ (or $\mathcal{K}=1$) for arbitrary input states of $N$ particles. The generalized bunching allows to certify in a \textit{polynomial} in $N$ number of runs that a physical device realizing Boson Sampling with \textit{an arbitrary} network operates in the regime of full quantum coherence compatible \textit{only} with completely indistinguishable bosons. The protocol needs \textit{only polynomial} classical computations for the standard Boson Sampling, whereas an \textit{analytic formula} is available for the scattershot version.

quant-ph↗

arXiv2015

Tight bound on trace distance between a realistic device with partially indistinguishable bosons and the ideal Boson Sampling

We study the closeness of an experimental unitary bosonic network with only partially indistinguishable bosons in an arbitrary mixed input state, in particular an experimental realization of the Boson Sampling, to the ideal bosonic network, where the measure of closeness of two networks is the trace distance between the output probability distributions. An upper bound on the trace distance to the ideal bosonic network is proven and also a bound on the difference between probabilities of an output configuration. Moreover, the upper bound on the trace distance is tight, provided that a physically transparent distinguishability conjecture is true. For a small distinguishability error it is shown that a realistic device with $N$ bosons is at a constant trace distance to the ideal Boson Sampling under the $O(N^{-1})$-scaling of the mismatch of internal states of bosons.

quant-ph↗

arXiv2015

Partial indistinguishability theory for multi-photon experiments in multiport devices

We generalize an approach for description of multi-photon experiments with multi-port unitary linear optical devices, initiated in \textit{Phys. Rev. A \textbf{89}, 022333 (2014)} for the case of single photons in mixed spectral states, to arbitrary (multi-photon) input and arbitrary photon detectors. We give a physical interpretation of a non-negative definite Hermitian matrix, the matrix of a quadratic form giving output probabilities, as the partial indistinguishability matrix. We show that output probabilities are \textit{always} given in terms of the matrix permanents of the Hadamard product of network matrix and matrices depending on spectral state of photons and spectral sensitivities of detectors. Moreover, in case of input with up to one photon per mode, the output probabilities are given by a sum (or integral) with each term being the absolute value squared of such a matrix permanent. We conjecture that, for an arbitrary multi-photon input, zero output probability of an output configuration is \textit{always} the result of an exact cancellation of quantum transition amplitudes of completely indistinguishable photons (a subset of all input photons) and, moreover, \textit{does not depend} on coherence between only partially indistinguishable photons. The conjecture is supported by examples. Furthermore, we propose a measure of partial indistinguishability of photons which generalizes Mandel's observation, and find the law of degradation of quantum coherence in a realistic Boson-Sampling device with increase of the total number of photons and/or their "classicality parameter".

quant-ph↗

arXiv2014

Nonlinear Zeno dynamics due to atomic interactions in Bose-Einstein condensate

We show that nonlinear interactions induce both the Zeno and anti-Zeno effects in the generalised Bose-Josephson model (with the on-site interactions and the second-order tunneling) describing Bose-Einstein condensate in double-well trap subject to particle removal from one of the wells. We find that the on-site interactions induce \textit{only} the Zeno effect, which appears at long evolution times, whereas the second-order tunneling leads to a strong decay of the atomic population at short evolution times, reminiscent of the anti-Zeno effect, and destroys the nonlinear Zeno effect due to the on-site interactions at long times.

cond-mat.quant-gas↗

arXiv2014

Conditions for an experimental Boson-sampling computer to disprove the Extended Church-Turing thesis

We give a set of sufficient conditions on the experimental Boson-Sampling computer to satisfy Theorem 1.3 of Aaronson & Arkhipov (Theory of Computing \textbf{9}, 143 (2013)) stating a computational problem whose simulation on a classical computer would collapse the polynomial hierarchy of the computational complexity to the third level. This implies that such an experimental device is in conflict with the Extended Church-Turing thesis. In practical terms, we give a set of sufficient conditions for the scalability of the experimental Boson-Sampling computer beyond the power of the classical computers. The derived conditions can be also used for devising efficient verification tests of the Boson-Sampling computer.

quant-ph↗

arXiv2014

Explicit form of the Bayesian posterior estimate of a quantum state under the uninformative prior

An analytical solution for the posterior estimate in Bayesian tomography of the unknown quantum state of an arbitrary quantum system (with a finite-dimensional Hilbert space) is found. First, we derive the Bayesian estimate for a pure quantum state measured by a set of arbitrary rank-1 POVMs under the uninformative (i.e. the unitary invariant or Haar) prior. The expression for the estimate involves the matrix permanents of the Gram matrices with repeated rows and columns, with the matrix elements being the scalar products of vectors giving the measurement outcomes. Second, an unknown mixed state is treated by the Hilbert-Schmidt purification. In this case, under the uninformative prior for the combined pure state, the posterior estimate of the mixed state of the system is expressed through the matrix $α$-permanents of the Gram matrices of scalar products of vectors giving the measurement outcomes. In the mixed case, there is also a free integer parameter -- the Schmidt number -- which can be used to optimise the Bayesian reconstruction (for instance, in case of Schimdt number being equal to 1, the mixed state estimates reduces to the pure state estimate). We also discuss the perspectives of approximate numerical computation and asymptotic analytical evaluation of the Bayesian estimate using the derived formula.

quant-ph↗

arXiv2014

Asymptotic evaluation of bosonic probability amplitudes in linear unitary networks in the case of large number of bosons

An asymptotic analytical approach is proposed for bosonic probability amplitudes in unitary linear networks, such as the optical multiport devices for photons. The asymptotic approach applies for large number of bosons $N\gg M$ in the $M$-mode network, where $M$ is finite. The probability amplitudes of $N$ bosons unitarily transformed from the input modes to the output modes of a unitary network are expressed through a multidimensional integral with the integrand containing a large parameter (N) in the exponent. The integral representation allows an asymptotic estimate of bosonic probability amplitudes up to a multiplicative error of order 1/N by the saddle point method. The estimate depends on solution of the scaling problem for the $M\times M$-dimensional unitary network matrix: to find the left and right diagonal matrices which scale the unitary matrix to a matrix which has specified row and column sums (equal, respectively, to the distributions of bosons in the input and output modes). The scaled matrices give the saddle points of the integral. For simple saddle points, an explicit formula giving the asymptotic estimate of bosonic probability amplitudes is derived. Performance of the approximation and the scaling of the relative error with N are studied for two-mode network (the beam-splitter), where the saddle-points are roots of a quadratic and an exact analytical formula for the probability amplitudes is available, and for three-mode network (the tritter).

quant-ph↗

arXiv2014

Nondecaying linear and nonlinear modes in a periodic array of spatially localized dissipations

We demonstrate the existence of extremely weakly decaying linear and nonlinear modes (i.e. modes immune to dissipation) in the one-dimensional periodic array of identical spatially localized dissipations, where the dissipation width is much smaller than the period of the array. We consider wave propagation governed by the one-dimensional Schrödinger equation in the array of identical Gaussian-shaped dissipations with three parameters, the integral dissipation strength $Γ_0$, the width $σ$ and the array period $d$. In the linear case, setting $σ\to0$, while keeping $Γ_0$ fixed, we get an array of zero-width dissipations given by the Dirac delta-functions, i.e. the complex Kroning-Penney model, where an infinite number of nondecaying modes appear with the Bloch index being either at the center, $k= 0$, or at the boundary, $k= π/d $, of an analog of the Brillouin zone. By using numerical simulations we confirm that the weakly decaying modes persist for $σ$ such that $σ/d\ll1$ and have the same Bloch index. The nondecaying modes persist also if a real-valued periodic potential is added to the spatially periodic array of dissipations, with the period of the dissipative array being multiple of that of the periodic potential. We also consider evolution of the soliton-shaped pulses in the nonlinear Schrödinger equation with the spatially periodic dissipative lattice and find that when the pulse width is much larger than the lattice period and its wave number $k$ is either at the center, $k= 2π/d$, or at the boundary, $k= π/d $, a significant fraction of the pulse escapes the dissipation forming a stationary nonlinear mode with the soliton shaped envelope and the Fourier spectrum consisting of two peaks centered at $k $ and $-k$.

math-ph↗

arXiv2013

The quantum de Finetti representation for the Bayesian Quantum Tomography and the Quantum Discord

We point out that the quantum de Finetti representation, unique for infinitely extendable exchangeable systems, assigns a non-zero Quantum Discord to uncorrelated systems and thus cannot serve as an universal prior distribution in the Bayesian Quantum Tomography. This apparent paradox stems from linearity of the Born rule for the probability assignment in Quantum Mechanics, which results in mixing of one's knowledge about the quantum state and the representative of the state in one density matrix.

quant-ph↗

arXiv2013

Thermal noise for quantum state inference

In this work we describe a simple and efficient scheme for inference of photon number distribution by adding variable thermal noise to the signal. The inference remains feasible even if the scheme parameters are subject to random dynamical change.

quant-ph↗

arXiv2012

Nonlinear dissipation can combat linear loss

We demonstrate that it is possible to compensate for effects of strong linear loss when generating non-classical states by engineered nonlinear dissipation. We show that it is always possible to construct such a loss-resistant dissipative gadget in which, for a certain class of initial states, the desired non-classical pure state can be attained within a particular time interval with an arbitrary precision. Further we demonstrate that an arbitrarily large linear loss can still be compensated by a sufficiently strong coherent or even thermal driving, thus attaining a strongly non-classical (in particular, sub-Poissonian) stationary mixed states.

quant-ph↗

arXiv2012

State engineering of Bose-Einstein condensate in the optical lattice by a periodic sublattice of dissipative sites

We introduce the notion of dissipative periodic lattice as an optical lattice with periodically distributed dissipative sites and argue that it allows to engineer unconventional Bose-Einstein superfluids with the complex-valued order parameter. We consider two examples, the one-dimensional dissipative optical lattice, where each third site is dissipative, and the dissipative honeycomb optical lattice, where each dissipative lattice site neighbors three non-dissipated sites. The tight-binding approximation is employed, which allows one to obtain analytical results. In the one-dimensional case the condensate is driven to a coherent Bloch-like state with non-zero quasimomentum, which breaks the translational periodicity of the dissipative lattice. In the two-dimensional case the condensate is driven to a zero quasimomentum Bloch-like state, which is a coherent superposition of four-site discrete vortices of alternating vorticity with the vortex centers located at the dissipative sites.

cond-mat.quant-gas↗

arXiv2012

State diagram and the phase transition of $p$-bosons in a square bi-partite optical lattice

It is shown that, in a reasonable approximation, the quantum state of $p$-bosons in a bi-partite square two-dimensional optical lattice is governed by the nonlinear boson model describing tunneling of \textit{boson pairs} between two orthogonal degenerate quasi momenta on the edge of the first Brillouin zone. The interplay between the lattice anisotropy and the atomic interactions leads to the second-order phase transition between the number-squeezed and coherent phase states of the $p$-bosons. In the isotropic case of the recent experiment, Nature Physicis 7, 147 (2011), the $p$-bosons are in the coherent phase state, where the relative global phase between the two quasi momenta is defined only up to mod($π$): $ϕ=\pmπ/2$. The quantum phase diagram of the nonlinear boson model is given.

cond-mat.quant-gas↗