Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1811.07721 · Physical Review A

Preserving measurements for optimal state discrimination over quantum channels

Spiros Kechrimparis, Tanmay Singal, Chahan M. Kropf, Joonwoo Bae

Published Jun 3, 2019• 11 citations
arXivHTMLPDF

Abstract

In this work, we consider optimal discrimination among quantum states that are sent through a quantum channel. We show the conditions on a quantum channel and an ensemble of states to preserve a measurement for optimal state discrimination over the channel. In particular, we show that for an ensemble of states where the states are given with equal a priori probabilities, an optimal measurement can be preserved over any quantum channel by applying local operations and classical communication, that is, by manipulating the quantum states before and after the channel application. Examples are provided for illustration in the case of quantum communication protocols. Our results can be readily applied to optimal state discrimination over various types of noise.

DOI
10.1103/physreva.99.062302

Related papers

Optimal measurement preserving qubit channels

Spiros Kechrimparis, Joonwoo Bae

Abstract We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the characterization of optimal measurement preserving (OMP) channels for a given qubit ensemble, e.g., a set of two states or a set of multiple qubit states with equal a priori probabilities. Conversely, we also characterize qubit ensembles for which a given channel is OMP, such as unitary and depolarization channels. Finally, we show how the sets of OMP channels for a given ensemble can be constructed.

arXiv:2006.16366•New Journal of Physics•Nov 20, 2020•2 citations

Channel Coding of a Quantum Measurement

Spiros Kechrimparis, Chahan M. Kropf, Filip Wudarski +1 more

In this work, we consider the preservation of a measurement for quantum systems interacting with an environment. Namely, a method of preserving an optimal measurement over a channel is devised, what we call channel coding of a quantum measurement in that operations are applied before and after a channel in order to protect a measurement. A protocol that preserves a quantum measurement over an arbitrary channel is shown only with local operations and classical communication without the use of a larger Hilbert space. Therefore, the protocol is readily feasible with present day's technologies. Channel coding of qubit measurements is presented, and it is shown that a measurement can be preserved for an arbitrary channel for both i) pairs of qubit states and ii) ensembles of equally probable states. The protocol of preserving a quantum measurement is demonstrated with IBM quantum computers.

arXiv:1908.10735•IEEE Journal on Selected Areas in Communications•Jan 24, 2020•13 citations

Optimal state discrimination over quantum channels

Joonwoo Bae

Quantum state discrimination is a fundamental task in quantum information theory and also an important building block in practical quantum information applications. We here consider optimal state discrimination in a noisy environment in which quantum states may be corrupted due to the intervention of an environment. We show that even if there exists an unwanted interaction with an environment and the channel describing the interaction is not yet identified, a measurement prepared in the beginning for optimal state discrimination can be preserved as an optimal measurement ever after a channel use. This means that in a practical realization of quantum communication, verification of a channel can be circumvented and the cost of quantum tomography is saved. We also show a protocol of preserving an optimal measurement for state discrimination.

Quantum Communications and Quantum Imaging•Sep 6, 2019•0 citations

Optimal discrimination of quantum states

Graeme Weir

Quantum state discrimination is a fundamental task in the field of quantum communication and quantum information theory. Unless the states to be discriminated are mutually orthogonal, there will be some error in any attempt to determine which state was sent. Several strategies to optimally discriminate between quantum states exist, each maximising some figure of merit. In this thesis we mainly investigate the minimum-error strategy, in which the probability of correctly guessing the signal state is maximised. We introduce a method for constructing the optimal Positive-Operator Valued Measure (POVM) for this figure of merit, which is applicable for arbitrary states and arbitrary prior probabilities. We then use this method to solve minimum-error state discrimination for the so-called trine states with arbitrary prior probabilities - the first such general solution for a set of quantum states since the two-state case was solved when the problem of state discrimination was first introduced. We also investigate the difference between local and global measurements for a bipartite ensemble of states, and find that in certain circumstances the local measurement is superior. We conclude by finding a bipartite analogue to the Helstrom conditions, which indicate when a POVM satisfies the minimum-error criteria.

•Jan 1, 2018•4 citations

State and Measurement Design for Quantum Detection Over Quantum Channels

Jeremy Johnston, Xiaodong Wang

In quantum state discrimination, typically the design of measurement operators or probe state is formulated assuming the set of possible states is perfectly known, but this may yield designs which are sensitive to deviations in the realized set of states. For example, the channel through which a transmitted state is sent may not be deterministic, but instead characterized by a classical distribution over quantum channels. In this paper, we consider the design of measurement schemes and probe states for quantum detection over an uncertain quantum channel. We present stochastic gradient-based algorithms to maximize the expected performance over the channel distribution for various design objectives, including the detection probability and mutual information. Furthermore, we introduce a scheme that leverages the isometric extension of a quantum channel to measure the channel output in an enlarged Hilbert space such that the channels are more distinguishable, while simultaneously reducing the effective dimension and thereby reducing the optimization complexity. Finally, we apply the proposed algorithms to multicopy channel discrimination.

IEEE International Symposium on Information Theory (ISIT)•Jun 22, 2025•0 citations

Entanglement in channel discrimination with restricted measurements

William Matthews, Marco Piani, John Watrous

We study the power of measurements implementable with local quantum operations and classical communication (LOCC) measurements in the setting of quantum channel discrimination. More precisely, we consider discrimination procedures that attempt to identify an unknown channel, chosen uniformly from two known alternatives, that take the following form: (i) the input to the unknown channel is prepared in a possibly entangled state with an ancillary system, (ii) the unknown channel is applied to the input system, and (iii) an LOCC measurement is performed on the output and ancillary systems, resulting in a guess for which of the two channels was given. The restriction of the measurement in such a procedure to be an LOCC measurement is of interest because it isolates the entanglement in the initial input-ancillary systems as a resource in the setting of channel discrimination. We prove that there exist channel discrimination problems for which restricted procedures of this sort can be at either of the two extremes: they may be optimal within the set of all discrimination procedures (and simultaneously outperform all strategies that make no use of entanglement), or they may be no better than unentangled strategies (and simultaneously suboptimal within the set of all discrimination procedures).

arXiv:1004.0888•Physical Review A•Sep 7, 2010•29 citations
In this work, we consider optimal discrimination among quantum states that are sent through a quantum channel. We show the conditions on a quantum channel and an ensemble of states to preserve a measurement for optimal state discrimination over the channel. In particular, we show that for an ensemble of states where the states are given with equal a priori probabilities, an optimal measurement can be preserved over any quantum channel by applying local operations and classical communication, that is, by manipulating the quantum states before and after the channel application. Examples are provided for illustration in the case of quantum communication protocols. Our results can be readily applied to optimal state discrimination over various types of noise.
Abstract We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the characterization of optimal measurement preserving (OMP) channels for a given qubit ensemble, e.g., a set of two states or a set of multiple qubit states with equal a priori probabilities. Conversely, we also characterize qubit ensembles for which a given channel is OMP, such as unitary and depolarization channels. Finally, we show how the sets of OMP channels for a given ensemble can be constructed.
In this work, we consider the preservation of a measurement for quantum systems interacting with an environment. Namely, a method of preserving an optimal measurement over a channel is devised, what we call channel coding of a quantum measurement in that operations are applied before and after a channel in order to protect a measurement. A protocol that preserves a quantum measurement over an arbitrary channel is shown only with local operations and classical communication without the use of a larger Hilbert space. Therefore, the protocol is readily feasible with present day's technologies. Channel coding of qubit measurements is presented, and it is shown that a measurement can be preserved for an arbitrary channel for both i) pairs of qubit states and ii) ensembles of equally probable states. The protocol of preserving a quantum measurement is demonstrated with IBM quantum computers.
Quantum state discrimination is a fundamental task in quantum information theory and also an important building block in practical quantum information applications. We here consider optimal state discrimination in a noisy environment in which quantum states may be corrupted due to the intervention of an environment. We show that even if there exists an unwanted interaction with an environment and the channel describing the interaction is not yet identified, a measurement prepared in the beginning for optimal state discrimination can be preserved as an optimal measurement ever after a channel use. This means that in a practical realization of quantum communication, verification of a channel can be circumvented and the cost of quantum tomography is saved. We also show a protocol of preserving an optimal measurement for state discrimination.
Quantum state discrimination is a fundamental task in the field of quantum communication and quantum information theory. Unless the states to be discriminated are mutually orthogonal, there will be some error in any attempt to determine which state was sent. Several strategies to optimally discriminate between quantum states exist, each maximising some figure of merit. In this thesis we mainly investigate the minimum-error strategy, in which the probability of correctly guessing the signal state is maximised. We introduce a method for constructing the optimal Positive-Operator Valued Measure (POVM) for this figure of merit, which is applicable for arbitrary states and arbitrary prior probabilities. We then use this method to solve minimum-error state discrimination for the so-called trine states with arbitrary prior probabilities - the first such general solution for a set of quantum states since the two-state case was solved when the problem of state discrimination was first introduced. We also investigate the difference between local and global measurements for a bipartite ensemble of states, and find that in certain circumstances the local measurement is superior. We conclude by finding a bipartite analogue to the Helstrom conditions, which indicate when a POVM satisfies the minimum-error criteria.
In quantum state discrimination, typically the design of measurement operators or probe state is formulated assuming the set of possible states is perfectly known, but this may yield designs which are sensitive to deviations in the realized set of states. For example, the channel through which a transmitted state is sent may not be deterministic, but instead characterized by a classical distribution over quantum channels. In this paper, we consider the design of measurement schemes and probe states for quantum detection over an uncertain quantum channel. We present stochastic gradient-based algorithms to maximize the expected performance over the channel distribution for various design objectives, including the detection probability and mutual information. Furthermore, we introduce a scheme that leverages the isometric extension of a quantum channel to measure the channel output in an enlarged Hilbert space such that the channels are more distinguishable, while simultaneously reducing the effective dimension and thereby reducing the optimization complexity. Finally, we apply the proposed algorithms to multicopy channel discrimination.
We study the power of measurements implementable with local quantum operations and classical communication (LOCC) measurements in the setting of quantum channel discrimination. More precisely, we consider discrimination procedures that attempt to identify an unknown channel, chosen uniformly from two known alternatives, that take the following form: (i) the input to the unknown channel is prepared in a possibly entangled state with an ancillary system, (ii) the unknown channel is applied to the input system, and (iii) an LOCC measurement is performed on the output and ancillary systems, resulting in a guess for which of the two channels was given. The restriction of the measurement in such a procedure to be an LOCC measurement is of interest because it isolates the entanglement in the initial input-ancillary systems as a resource in the setting of channel discrimination. We prove that there exist channel discrimination problems for which restricted procedures of this sort can be at either of the two extremes: they may be optimal within the set of all discrimination procedures (and simultaneously outperform all strategies that make no use of entanglement), or they may be no better than unentangled strategies (and simultaneously suboptimal within the set of all discrimination procedures).