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Physical Review A

Sequential quantum maximum-confidence discrimination

Hanwool Lee, Kieran Flatt, Joonwoo Bae

Published Nov 6, 2025• 5 citations
Publisher

Abstract

Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we investigate a sequential scenario of quantum state discrimination with maximum confidence, called maximum-confidence discrimination, which generalizes other strategies such as minimum-error and unambiguous discrimination. We show that sequential discrimination with equally high confidence can be realized if and only if positive-operator-valued measure elements for a maximum-confidence measurement can be unambiguously discriminated, i.e., linearly independent; otherwise, a party will have strictly less confidence in measurement outcomes than the previous one. We investigate the tradeoff between state disturbance and information gain in sequential state discrimination and show that the less guessing probability there is from conclusive outcomes for each party, the more parties can participate in the sequential scenario.

DOI
10.1103/wm73-g73w

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Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we investigate a sequential scenario of quantum state discrimination with maximum confidence, called maximum-confidence discrimination, which generalizes other strategies such as minimum-error and unambiguous discrimination. We show that sequential discrimination with equally high confidence can be realized if and only if positive-operator-valued measure elements for a maximum-confidence measurement can be unambiguously discriminated, i.e., linearly independent; otherwise, a party will have strictly less confidence in measurement outcomes than the previous one. We investigate the tradeoff between state disturbance and information gain in sequential state discrimination and show that the less guessing probability there is from conclusive outcomes for each party, the more parties can participate in the sequential scenario.
Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we investigate a sequential scenario of quantum state discrimination with maximum confidence, called maximum-confidence discrimination, which generalizes other strategies including minimum-error and unambiguous state discrimination. We show that sequential state discrimination with equally high confidence can be realized only when positive-operator-valued measure elements for a maximum-confidence measurement are linearly independent; otherwise, a party will have strictly less confidence in measurement outcomes than the previous one. We establish a tradeoff between the disturbance of states and information gain in sequential state discrimination, namely, that the less a party learn in state discrimination in terms of a guessing probability, the more parties can participate in the sequential scenario.
One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between nonorthogonal quantum states.In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum-confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination.We first show that maximum-confidence discrimination, as well as unambiguous discrimination, contains contextual advantages.We then consider a semi-device-independent scenario of certifying maximum-confidence measurement.The scenario naturally contains undetected events, making it a natural setting to explore maximum-confidence measurements.We show that the certified maximum confidence in quantum theory also contains contextual advantages.Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.
Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme that enables multiple parties to share quantum uncertainty, in terms of the max relative entropy, generated by a single party. Our scheme is based upon maximum-confidence measurements and takes advantages of weak measurements to allow a number of parties to perform state discrimination on a single quantum system. We review known sequential state discrimination and show how our scheme would work through a number of examples where ensembles may or may not contain symmetries. Our results will have a role to play in understanding the ultimate limits of sequential information extraction and guide the development of quantum resource sharing in sequential settings.
Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive outcomes across various guessing strategies. For minimum-error discrimination, the advantage is in terms of the confidences of individual outcomes, while for unambiguous state discrimination, it is in terms of the average guessing probability. For maximum-confidence discrimination, we show that contextual advantages occur not only for the confidence but also their average, the guessing probability, as well as the inconclusive outcome rate. Our results show that contextual advantages are observed across all two-state discrimination schemes and figures of merit. We envisage that various quantum information applications based on state discrimination may offer advantages over noncontextual theories.
Nonorthogonal quantum states cannot be perfectly distinguished; seeking the optimal discrimination strategy is a critical task in quantum information processing. Maximum-confidence measurements provide the highest confidence that represents the conditional probability of the prepared state being correct given an observed outcome. In this work, we experimentally investigate maximum-confidence measurements by discrete-time quantum walks for geometrically uniform states and tetrahedron states, and our experimental results clearly show that the maximum-confidence measurements coincide with minimum-error discrimination in these cases. Meanwhile, we also provide experimental evidence for the contextual advantage of maximum-confidence measurements in quantum theory over classical theory, using two quantum pure states as an example. Our work provides a unified experimental approach to quantum state discrimination that highlights the practical value of maximum-confidence measurements in quantum information processing.
In quantum state discrimination, one aims to identify unknown states from a given ensemble by performing measurements. Different strategies such as minimum-error discrimination or unambiguous state identification find different optimal measurements. Maximum-confidence measurements (MCMs) maximize the confidence with which inputs can be identified given the measurement outcomes. This unifies a range of discrimination strategies including minimum-error and unambiguous state identification, which can be understood as limiting cases of MCM. In this work we investigate MCMs for general ensembles of qubit states. We present a method for finding MCMs for qubit-state ensembles by exploiting their geometry and apply it to several interesting cases, including ensembles of two and four mixed states and ensembles of an arbitrary number of pure states. We also compare MCMs to minimum-error and unambiguous discrimination for qubits. Our results provide interpretations of various qubit measurements in terms of MCM and can be used to devise qubit protocols.