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Physical Review Research

Quantum resources for assisted optimal state discrimination

O. Jiménez, M. A. Solís-Prosser, A. Delgado, Leonardo Neves

Published Dec 23, 2024• 2 citations
Publisher

Abstract

We revisit the discussion of the quantum resources required to perform optimal unambiguous discrimination between two nonorthogonal quantum states when the protocol is assisted by an auxiliary system (ancilla). Initially, the formulation of the problem led to the assumption that entanglement between the main system and the ancilla was the key resource for the task. However, it was later shown that entanglement is not necessary at all, while quantum dissonance may or may not be required, depending on the relationship between the overlap and the probabilities of the inputs [Zhang, ]. Here, we show that, regardless of this relationship, coherence and purity are required resources for the task and thus more fundamental than dissonance. Coherence is analyzed based on its generalized resource theory, which allowed us to find the scenario that generates the maximal cryptographic randomness gain in the protocol. Purity, on the other hand, is shown to be greater than coherence when both measures are defined via the same distance, including the extreme cases of orthogonal and parallel states, where the latter is zero. Therefore, we conclude that purity is the most fundamental resource for assisted optimal state discrimination. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043303

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We revisit the discussion of the quantum resources required to perform optimal unambiguous discrimination between two nonorthogonal quantum states when the protocol is assisted by an auxiliary system (ancilla). Initially, the formulation of the problem led to the assumption that entanglement between the main system and the ancilla was the key resource for the task. However, it was later shown that entanglement is not necessary at all, while quantum dissonance may or may not be required, depending on the relationship between the overlap and the probabilities of the inputs [Zhang, ]. Here, we show that, regardless of this relationship, coherence and purity are required resources for the task and thus more fundamental than dissonance. Coherence is analyzed based on its generalized resource theory, which allowed us to find the scenario that generates the maximal cryptographic randomness gain in the protocol. Purity, on the other hand, is shown to be greater than coherence when both measures are defined via the same distance, including the extreme cases of orthogonal and parallel states, where the latter is zero. Therefore, we conclude that purity is the most fundamental resource for assisted optimal state discrimination. Published by the American Physical Society 2024
Roa et al. showed that quantum state discrimination between two nonorthogonal quantum states does not require quantum entanglement but quantum dissonance only. We find that quantum coherence can also be utilized for unambiguous quantum state discrimination. We present a protocol and quantify the required coherence for this task. We discuss the optimal unambiguous quantum state discrimination strategy in some cases. In particular, our work illustrates an avenue to find the optimal strategy for discriminating two nonorthogonal quantum states by measuring quantum coherence.
Unambiguous quantum state discrimination (UQSD), assisted by an auxiliary system, generally requires quantum correlations as a resource. We find that quantum coherence can be utilized as a resource in an allied UQSD protocol that is devoid of quantum correlations. We propose a mechanism for quantum state discrimination where the non-orthogonality of the input states can be converted to quantum coherence of the auxiliary system. We quantify the required coherence generated during this and the optimal unambiguous quantum state discrimination strategy in some specific cases. In particular, our result introduces how to find the optimal strategy by measuring quantum coherence in protocols that discriminates between two non-orthogonal quantum states.
Unambiguous quantum state discrimination (UQSD), assisted by an auxiliary system, generally requires quantum correlations as a resource. We find that quantum coherence can be utilized as a resource in an allied UQSD protocol that is devoid of quantum correlations. We propose a mechanism for quantum state discrimination where the non-orthogonality of the input states can be converted to quantum coherence of the auxiliary system. We quantify the required coherence generated during this and the optimal unambiguous quantum state discrimination strategy in some specific cases. In particular, our result introduces how to find the optimal strategy by measuring quantum coherence in protocols that discriminates between two non-orthogonal quantum states.
The optimal measurement that discriminates nonorthogonal quantum states with fixed rates of inconclusive outcomes (FRIO) can be decomposed into an assisted separation of the inputs, yielding conclusive and inconclusive outputs, followed by a minimum-error (ME) measurement for the conclusive ones (standard FRIO) or both ones (concatenated FRIO). The implementation of these measurements is underpinned by quantum resources, and here we investigate coherence based on positive operator-valued measures (POVMs) as a resource for both strategies in discriminating equally probable symmetric states of arbitrary dimension. First, we show that the POVM coherence in the assisted separation stage decomposes into the coherence of the ancillary state and the quantum discord between the system and the ancilla, evidencing coherence as a more elementary resource than quantum correlations. Next, it is demonstrated that the POVM coherence for standard and concatenated FRIO decomposes into the POVM coherence measures for state separation and ME measurement, weighted by the probabilities of occurrence of each event. Due to the ME discrimination of inconclusive states, the coherence required for the concatenated scheme is shown to be greater than that of the standard one. We discuss other general aspects of our results by characterizing the POVM coherence in the discrimination of qutrit states, with respect to the distinguishability of the inputs and the inconclusive rate. Finally, by exploiting POVM-based coherence as a quantifier of cryptographic randomness gain, we discuss the standard and concatenated FRIO strategies from the perspective of generating random bits that are secret to an eavesdropper.
State discrimination is one of the key steps in quantum information tasks. This paper introduces the assisted quantum entanglement to achieve this step. For this purpose, the paper introduces some preliminary knowledge to help enter the research topic, such as the matrix rank, Kronecker product, quantum states and the calculation method of Schmidt decomposition and rank. The latter involves the Singular value decomposition in matrix factorization theory. The method of distinguishing orthogonal states in single and many-body systems is also introduced, by using the so-called positive operator-valued measurements. Then the paper proves the fact that single or multipartite system non-orthogonal states are indistinguishable regardless of whether there are auxiliary resources, which may be either separable or entangled states. The paper further illustrates the feasibility of maximum entangled states acting on two-body systems and gives corresponding examples. At the same time, the feasibility of auxiliary resources for smaller entanglement is also investigated.
We consider how the theory of optimal quantum measurements determines the maximum information available to the receiving party of a quantum key distribution (QKD) system employing linearly independent but nonorthogonal quantum states. Such a setting is characteristic of several practical QKD protocols. Due to nonorthogonality, the receiver is not able to discriminate unambiguously between the signals. To understand the fundamental limits that this imposes, the quantity of interest is the maximum mutual information between the transmitter (Alice) and the receiver, whether legitimate (Bob) or an eavesdropper (Eve). To find the optimal measurement—taken individually or collectively—we use a framework based on operator algebra and general results derived from singular-value decomposition, achieving optimal solutions for von Neumann measurements and positive operator-valued measures (POVMs). The formal proof and quantitative analysis elaborated for two signals allow us to conclude that optimal von Neumann measurements are uniquely defined and provide a higher information gain compared to POVMs. Interestingly, collective measurements not only do not provide additional information gain with respect to individual ones but also suffer from a gain reduction in the case of POVMs. Published by the American Physical Society 2024