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arXiv:2412.17435 · Journal of the Korean Physical Society

Postmeasurement information and nonlocality of quantum state discrimination

Jinhyeok Heo, Donghoon Ha, Jeong San Kim

Published Oct 6, 2026• 0 citations
arXivHTMLPDF
DOI
10.1007/s40042-026-01735-0

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We consider a special form of state discrimination in which after the measurement we are given additional information that may help us identify the state. This task plays a central role in the analysis of quantum cryptographic protocols in the noisy-storage model, where the identity of the state corresponds to a certain bit string, and the additional information is typically a choice of encoding that is initially unknown to the cheating party. We first provide simple optimality conditions for measurements for any such problem and show upper and lower bounds on the success probability. For a certain class of problems, we furthermore provide tight bounds on how useful postmeasurement information can be. In particular, we show that for this class finding the optimal measurement for the task of state discrimination with postmeasurement information does in fact reduce to solving a different problem of state discrimination without such information. However, we show that for the corresponding classical state discrimination problems with postmeasurement information such a reduction is impossible, by relating the success probability to the violation of Bell inequalities. This suggests the usefulness of postmeasurement information as another feature that distinguishes the classical from a quantum world.
We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement setup after Alice has announced him the chosen ensemble, or he is forced to perform the measurement before Alice's announcement. In the latter case, he can only postprocess his measurement outcome when Alice's extra information becomes available. We compare the optimal guessing probabilities in the two scenarios, and we prove that they are the same if and only if there exist compatible (i.e., jointly measurable) optimal measurements for all of Alice's state ensembles. When this is the case, postprocessing any of the corresponding joint measurements is Bob's optimal strategy in the postmeasurement information scenario. Furthermore, we establish a connection between discrimination with postmeasurement information and the standard state discrimination. By means of this connection and exploiting the presence of symmetries, we are able to compute the various guessing probabilities in many concrete examples.
Nonlocality without entanglement (NLWE) is a nonlocal quantum phenomenon that arises in separable state discrimination. We show that the availability of the postmeasurement information about the prepared subensemble can affect the occurrence of NLWE in discriminating non-orthogonal nonentangled states. We provide a two-qubit state ensemble consisting of four nonorthogonal separable pure states and show that the postmeasurement information about the prepared subensemble can annihilate NLWE. We also provide another two-qubit state ensemble consisting of four nonorthogonal separable states and show that the postmeasurement information can create NLWE. Our result can provide a useful method to share or hide information using nonorthogonal separable states.