Implementation of POVMs by Projective Measurements and Postselection:Optimal Strategies and Applications to Unambiguous State Discrimination

We present new results concerning simulation of general quantum measurements (POVMs) by projective measurements (PMs) for the task of Unambiguous State Discrimination (USD). We formulate a problem of finding optimal strategy of simulation for given quantum measurement. The problem can be solved for qubit and qutrits measurements by Semi-Definite Programming (SDP) methods.

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Does Decoherence Select the Pointer Basis of a Quantum Meter?

Entropy ◽

10.3390/e24010106 ◽

2022 ◽

Vol 24 (1) ◽

pp. 106

Author(s):

Abraham G. Kofman ◽

Gershon Kurizki

Keyword(s):

Quantum Mechanics ◽

Quantum State ◽

Quantum Measurement ◽

Measurement Theory ◽

Quantum Measurements ◽

Quantum Measurement Theory ◽

Measuring Device ◽

Standard Quantum ◽

Pointer States ◽

Projective Measurements

The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.

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Decoherence and its role in the modern measurement problem

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2011.0490 ◽

2012 ◽

Vol 370 (1975) ◽

pp. 4576-4593 ◽

Cited By ~ 16

Author(s):

David Wallace

Keyword(s):

Wave Function ◽

Quantum Mechanics ◽

Quantum Measurement ◽

Measurement Problem ◽

Scientific Practice ◽

Measurement Theory ◽

Quantum Measurements ◽

Quantum Measurement Problem ◽

Modern Physics ◽

Conceptual Problems

Decoherence is widely felt to have something to do with the quantum measurement problem, but getting clear on just what is made difficult by the fact that the ‘measurement problem’, as traditionally presented in foundational and philosophical discussions, has become somewhat disconnected from the conceptual problems posed by real physics. This, in turn, is because quantum mechanics as discussed in textbooks and in foundational discussions has become somewhat removed from scientific practice, especially where the analysis of measurement is concerned. This paper has two goals: firstly (§§1–2), to present an account of how quantum measurements are actually dealt with in modern physics (hint: it does not involve a collapse of the wave function) and to state the measurement problem from the perspective of that account; and secondly (§§3–4), to clarify what role decoherence plays in modern measurement theory and what effect it has on the various strategies that have been proposed to solve the measurement problem.

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Quantum-Heat Fluctuation Relations in Three-Level Systems Under Projective Measurements

Condensed Matter ◽

10.3390/condmat5010017 ◽

2020 ◽

Vol 5 (1) ◽

pp. 17 ◽

Cited By ~ 1

Author(s):

Guido Giachetti ◽

Stefano Gherardini ◽

Andrea Trombettoni ◽

Stefano Ruffo

Keyword(s):

Energy Scale ◽

Quantum Measurements ◽

Thermal Component ◽

Initial State ◽

Fluctuation Relations ◽

N Level ◽

Two Level Systems ◽

Jarzynski Equality ◽

Projective Measurements

We study the statistics of energy fluctuations in a three-level quantum system subject to a sequence of projective quantum measurements. We check that, as expected, the quantum Jarzynski equality holds provided that the initial state is thermal. The latter condition is trivially satisfied for two-level systems, while this is generally no longer true for N-level systems, with N > 2 . Focusing on three-level systems, we discuss the occurrence of a unique energy scale factor β eff that formally plays the role of an effective inverse temperature in the Jarzynski equality. To this aim, we introduce a suitable parametrization of the initial state in terms of a thermal and a non-thermal component. We determine the value of β eff for a large number of measurements and study its dependence on the initial state. Our predictions could be checked experimentally in quantum optics.

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Unambiguous State Discrimination in Quantum Key Distribution Based on Time Coding

Journal of Applied Spectroscopy ◽

10.1007/s10812-019-00897-z ◽

2019 ◽

Vol 86 (5) ◽

pp. 806-809 ◽

Cited By ~ 1

Author(s):

M. M. Eskandari ◽

D. B. Horoshko ◽

S. Ya. Kilin

Keyword(s):

Quantum Key Distribution ◽

Key Distribution ◽

State Discrimination ◽

Time Coding ◽

Unambiguous State Discrimination

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Operational Algorithms for Separable Qubit X States

Condensed Matter ◽

10.3390/condmat4030064 ◽

2019 ◽

Vol 4 (3) ◽

pp. 64

Author(s):

Demosthenes Ellinas

Keyword(s):

State Space ◽

Quantum Measurement ◽

Unitary Operator ◽

Probability Distributions ◽

Quantum Walk ◽

Higher Order ◽

Quantum Measurements ◽

Uniform Hypergraph ◽

Extended State ◽

Quantum Polynomial

This work motivates and applies operational methodology to simulation of quantum statistics of separable qubit X states. Three operational algorithms for evaluating separability probability distributions are put forward. Building on previous findings, the volume function characterizing the separability distribution is determined via quantum measurements of multi-qubit observables. Three measuring states, one for each algorithm are generated via (i) a multi-qubit channel map, (ii) a unitary operator generated by a Hamiltonian describing a non-uniform hypergraph configuration of interactions among 12 qubits, and (iii) a quantum walk CP map in a extended state space. Higher order CZ gates are the only tools of the algorithms hence the work associates itself computationally with the Instantaneous Quantum Polynomial-time Circuits (IQP), while wrt possible implementation the work relates to the Lechner-Hauke-Zoller (LHZ) architecture of higher order coupling. Finally some uncertainty aspects of the quantum measurement observables are discussed together with possible extensions to non-qubit separable bipartite systems.

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Heralded orthogonalisation of coherent states and their conversion to discrete-variable superpositions

Quantum Measurements and Quantum Metrology ◽

10.1515/qmetro-2017-0005 ◽

2017 ◽

Vol 4 (1) ◽

pp. 35-43 ◽

Cited By ~ 1

Author(s):

Regina Kruse ◽

Christine Silberhorn ◽

Tim Bartley

Keyword(s):

Information Processing ◽

Quantum Information ◽

Coherent States ◽

Quantum Information Processing ◽

Fundamental Property ◽

Discrete Variable ◽

Successful Operation ◽

State Discrimination ◽

Unambiguous State Discrimination

Abstract The nonorthogonality of coherent states is a fundamental property which prevents them from being perfectly and deterministically discriminated. Here, we present an experimentally feasible protocol for the probabilistic orthogonalisation of a pair of coherent states, independent of their amplitude and phase. In contrast to unambiguous state discrimination, a successful operation of our protocol is heralded without measuring the states. As such, they remain suitable for further manipulation and the obtained orthogonal states serve as a discretevariable basis. Therefore, our protocol doubles as a simple continuous-to-discrete variable converter, which may find application in hybrid continuous-discrete quantum information processing protocols.

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