Quantum state discrimination, which seeks to correctly determine the state of a quantum system among a set of possible states through a finite number of measurements, has become fundamental for the increasing development of quantum technologies due to its underlying relation to various quantum information processing and communication tasks. In this work, we thoroughly explore the problem of distinguishing between two and three finite photon ensembles with identical compressed density operators, with a main focus on local solutions, i.e., with no entangling operations among ensemble photons. Using semidefinite programming, we provide optimal analytical and numerical discrimination strategies in the very low photon-number regime. Then, multiple approaches to an interferometry-based solution for the three-ensemble problem are analyzed based on existing experimental literature in single-photon polarization state discrimination. However, none of these approaches outperform a trivial extension to a well-known local solution of the two-ensemble problem given by d'Espagnat. An in-depth discussion on the local distinguishability of the three ensembles is given throughout the text. The results from these analyses suggest that more successful discrimination protocols require performing entangling operations among ensemble photons in order to exploit the inner correlations within each ensemble.Quantum state discrimination, which seeks to correctly determine the state of a quantum system among a set of possible states through a finite number of measurements, has become fundamental for the increasing development of quantum technologies due to its underlying relation to various quantum information processing and communication tasks. In this work, we thoroughly explore the problem of distinguishing between two and three finite photon ensembles with identical compressed density operators, with a main focus on local solutions, i.e., with no entangling operations among ensemble photons. Using semidefinite programming, we provide optimal analytical and numerical discrimination strategies in the very low photon-number regime. Then, multiple approaches to an interferometry-based solution for the three-ensemble problem are analyzed based on existing experimental literature in single-photon polarization state discrimination. However, none of these approaches outperform a trivial extension to a well-known local solution of the two-ensemble problem given by d'Espagnat. An in-depth discussion on the local distinguishability of the three ensembles is given throughout the text. The results from these analyses suggest that more successful discrimination protocols require performing entangling operations among ensemble photons in order to exploit the inner correlations within each ensemble.

Jan 1, 20250 citations

On Measurable Distinctions between Quantum Ensembles

Mark P. Silverman

Annals of the New York Academy of SciencesDec 1, 19862 citations

On the coherence veryfication of the continuous variable state in Fock space

Xiang‐Bin Wang, Keiji, Matsumoto, Tomita Akihisa

Almost all novel observable phenomena in quantum optics are related to the quantum coherence. The coherence here is determined by the relative phase inside a state. Unfortunately, so far all the relevant experimental results in quantum optics are insensitive to the phase information of the coherent state. Lack of phase information may cause serious consequences in many problems in quantum optics. For example, an ensemble of two mode squeezed states is a classical ensemble if the phase in each state is totally random; but it is a non-classical ensemble if the phase in each state is fixed. As a timly application, verification of this type of phase information in an ensemble of two mode squeezed states from the conventional laser is crucial to the validity of the continuous variavable quantum teleportation(CVQT) experiment. Here we give a simple scheme to distinguish two different ensemble of states: the Rudolph-Sanders ensemble, by which each squeezed states emitted has a uniform distribution from $0-2π$ on the phase value; and the van Enk-Fuchs ensemble, which emmits identical states with a fixed(but unknown) phase for every state. We believe our proposal can help to give a clear picture on whether the existing two mode squeezed states so far are indeed non-classical states which can be used as the entanglement resource.Almost all novel observable phenomena in quantum optics are related to the quantum coherence. The coherence here is determined by the relative phase inside a state. Unfortunately, so far all the relevant experimental results in quantum optics are insensitive to the phase information of the coherent state. Lack of phase information may cause serious consequences in many problems in quantum optics. For example, an ensemble of two mode squeezed states is a classical ensemble if the phase in each state is totally random; but it is a non-classical ensemble if the phase in each state is fixed. As a timly application, verification of this type of phase information in an ensemble of two mode squeezed states from the conventional laser is crucial to the validity of the continuous variavable quantum teleportation(CVQT) experiment. Here we give a simple scheme to distinguish two different ensemble of states: the Rudolph-Sanders ensemble, by which each squeezed states emitted has a uniform distribution from $0-2π$ on the phase value; and the van Enk-Fuchs ensemble, which emmits identical states with a fixed(but unknown) phase for every state. We believe our proposal can help to give a clear picture on whether the existing two mode squeezed states so far are indeed non-classical states which can be used as the entanglement resource.

arXiv:quant-ph/0203031Mar 7, 20020 citations

State Ensembles and Quantum Entropy

Subhash Kak

arXiv:1509.03220International Journal of Theoretical PhysicsJan 30, 201611 citations

Distinguishing synthetic unravelings on quantum computers

Eloy Piñol, Piotr Sierant, Dustin Keys +6 more

Distinct monitoring or intervention schemes can produce different conditioned stochastic quantum trajectories while sharing the same unconditional (ensemble-averaged) dynamics. This is the essence of unravelings of a given Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation: any trajectory-ensemble average of a function that is linear in the conditional state is completely determined by the unconditional density matrix, whereas applying a nonlinear function before averaging can yield unraveling-dependent results beyond the average evolution. A paradigmatic example is resonance fluorescence, where direct photodetection (jump/Poisson) and homodyne or heterodyne detection (diffusive/Wiener) define inequivalent unravelings of the same GKSL dynamics. In earlier work, we showed that nonlinear trajectory averages can distinguish such unravelings, but observing the effect in that optical setting requires demanding experimental precision. Here we translate the same idea to a digital setting by introducing synthetic unravelings implemented as quantum circuits acting on one and two qubits. We design two unravelings - a projective measurement unraveling and a random-unitary "kick" unraveling - that share the same ensemble-averaged evolution while yielding different nonlinear conditional-state statistics. We implement the protocols on superconducting-qubit hardware provided by IBM Quantum to access trajectory-level information. We show that the variance across trajectories and the ensemble-averaged von Neumann entropy distinguish the unravelings in both theory and experiment, while the unconditional state and the ensemble-averaged expectation values that are linear in the state remain identical. Our results provide an accessible demonstration that quantum trajectories encode information about measurement backaction beyond what is fixed by the unconditional dynamics.Distinct monitoring or intervention schemes can produce different conditioned stochastic quantum trajectories while sharing the same unconditional (ensemble-averaged) dynamics. This is the essence of unravelings of a given Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation: any trajectory-ensemble average of a function that is linear in the conditional state is completely determined by the unconditional density matrix, whereas applying a nonlinear function before averaging can yield unraveling-dependent results beyond the average evolution. A paradigmatic example is resonance fluorescence, where direct photodetection (jump/Poisson) and homodyne or heterodyne detection (diffusive/Wiener) define inequivalent unravelings of the same GKSL dynamics. In earlier work, we showed that nonlinear trajectory averages can distinguish such unravelings, but observing the effect in that optical setting requires demanding experimental precision. Here we translate the same idea to a digital setting by introducing synthetic unravelings implemented as quantum circuits acting on one and two qubits. We design two unravelings - a projective measurement unraveling and a random-unitary "kick" unraveling - that share the same ensemble-averaged evolution while yielding different nonlinear conditional-state statistics. We implement the protocols on superconducting-qubit hardware provided by IBM Quantum to access trajectory-level information. We show that the variance across trajectories and the ensemble-averaged von Neumann entropy distinguish the unravelings in both theory and experiment, while the unconditional state and the ensemble-averaged expectation values that are linear in the state remain identical. Our results provide an accessible demonstration that quantum trajectories encode information about measurement backaction beyond what is fixed by the unconditional dynamics.

quant-pharXiv:2601.19889Open Systems & Information DynamicsJan 28, 20260 citations

0-2π

on the phase value; and the van Enk-Fuchs ensemble, which emmits identical states with a fixed(but unknown) phase for every state. We believe our proposal can help to give a clear picture on whether the existing two mode squeezed states so far are indeed non-classical states which can be used as the entanglement resource.