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arXiv:2510.09381 · Reports on Progress in Physics

Structure of quantum measurements implementable with one round of classical communication

Arthur C. R. Dutra, Ties-A. Ohst, H. Chau Nguyen, Otfried Gühne

Published Mar 1, 2026• 0 citations
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Abstract

Measurements that can be implemented via local operations and classical communication (LOCC) constitute a class of operations that is available in future quantum networks in which parties share entangled resource states. We characterise the different classes of measurements implementable with LOCC, where communication is restricted to a single round with a fixed direction. In particular, using the framework of constrained separability problems, we provide a complete characterisation of the class of LOCC measurements that require one round of classical communication with a limit on the transmitted information. Furthermore, we show how to distinguish between adaptive and non-adaptive measurement strategies. Using our techniques, we present examples where the success probability of state discrimination depends on the direction of communication as well as on the message size. We also discuss explicit instances of state ensembles where non-projective measurements provide an advantage and where adaptive measurement strategies lead to improved success rates when compared to all non-adaptive strategies.

DOI
10.1088/1361-6633/ae4fef

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Measurements that can be implemented via local operations and classical communication (LOCC) constitute a class of operations that is available in future quantum networks in which parties share entangled resource states. We characterise the different classes of measurements implementable with LOCC, where communication is restricted to a single round with a fixed direction. In particular, using the framework of constrained separability problems, we provide a complete characterisation of the class of LOCC measurements that require one round of classical communication with a limit on the transmitted information. Furthermore, we show how to distinguish between adaptive and non-adaptive measurement strategies. Using our techniques, we present examples where the success probability of state discrimination depends on the direction of communication as well as on the message size. We also discuss explicit instances of state ensembles where non-projective measurements provide an advantage and where adaptive measurement strategies lead to improved success rates when compared to all non-adaptive strategies.
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We consider an infinite class of unambiguous quantum state discrimination problems on multipartite systems, described by Hilbert space H\mathcal{H}H, of any number of parties. Restricting consideration to measurements that act only on H\mathcal{H}H, we find the optimal global measurement for each element of this class, achieving the maximum possible success probability of 1/21/21/2 in all cases. This measurement turns out to be both separable and unique, and by our recently discovered necessary condition for local quantum operations and classical communication (LOCC) it is easily shown to be impossible by any finite-round LOCC protocol. We also show that, quite generally, if the input state is restricted to lie in H\mathcal{H}H, then any LOCC measurement on an enlarged Hilbert space is effectively identical to an LOCC measurement on H\mathcal{H}H. Therefore, our necessary condition for LOCC demonstrates directly that a higher success probability is attainable for each of these problems using general separable measurements as compared to that which is possible with any finite-round LOCC protocol.
We show that a pair of two-qubit product measurements can be perfectly distinguished when accessed jointly, yet cannot be perfectly distinguished when their local components are distributed between distant parties restricted to local quantum operations and classical communication (LOCC). This establishes a measurement analogue of nonlocality without entanglement that, unlike its state-based counterpart, emerges in a remarkably simple setting. We further uncover a hierarchy of LOCC discrimination strategies: adaptive protocols, in which the probe used at one site may depend on classical information obtained from another, can strictly outperform restricted non-adaptive protocols, as demonstrated by a set of six bipartite qutrit product measurements. We also show that LOCC distinguishability of bipartite measurements can be intrinsically directional, depending on which party initiates the protocol. More generally, we construct pairs of nnn-qubit product measurements that are globally perfectly distinguishable but cannot be perfectly distinguished across any bipartition, even when all parties on either side of the bipartition are allowed arbitrary joint quantum operations. Finally, we show how quantum data hiding based on quantum-process nonlocality without entanglement can be realized using elementary optical components.
We give a necessary condition that a separable measurement can be implemented by local quantum operations and classical communication (LOCC) in any finite number of rounds of communication, generalizing and strengthening a result obtained previously. That earlier result involved a bound that is tight when the number of measurement operators defining the measurement is relatively small. The present results generalize that bound to one that is tight for any finite number of measurement operators, and we also provide an extension which holds when that number is infinite. We apply these results to the famous example on a $3\ifmmode\times\else\texttimes\fi{}3$ system known as ``domino states,'' which were the first demonstration of nonlocality without entanglement. Our extended necessary condition provides another way of showing that these states cannot be perfectly distinguished by (finite-round) LOCC. It directly shows that this conclusion also holds for their related rotated domino states. We also introduce a class of problems involving the unambiguous discrimination of quantum states, each of which is an example where the states can be optimally discriminated by a separable measurement, but according to our condition, cannot be optimally discriminated by LOCC. These examples nicely illustrate the usefulness of the present results, since our earlier necessary condition, which the present result generalizes, is not strong enough to reach a conclusion in any of these cases.
In the absence of quantum channels, local operations on subsystems and classical communication between parties (LOCC) constitute the most general protocols available on spatially separated quantum systems. Every LOCC protocol implements a separable quantum measurement, but it is known that there exist separable measurements that cannot be implemented by LOCC. A longstanding problem in quantum information theory is to understand the difference between LOCC and the full set of separable measurements. Toward this end, we show in this paper how to construct an LOCC protocol to implement an arbitrary separable measurement whenever such a protocol exists. In addition, given a measurement that cannot be implemented by LOCC within some fixed maximum number of rounds, the method shows explicitly that this is the case.
Abstract Classical communication plays a crucial role to distinguish locally a class of quantum states. Despite considerable advances, we have very little knowledge about the number of measurement and communication rounds needed to implement a discrimination task by local quantum operations and classical communications (in short, LOCC). In this paper, we are able to show the relation between round numbers with the local discrimination of a set of pure bipartite orthogonal quantum states. To demonstrate the possible strong dependence on the round numbers, we consider a class of orthogonal product states in d ⊗ d , which require at least 2 d − 2 round of classical communications. Curiously the round number can be reduced to d by the assistance of one-ebit of entanglement as resource and can be reduced further by assistance of more entanglement. We are also able to show that the number of LOCC rounds needed for a discrimination task may depend on the amount of entanglement assistance.