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Quantum state discrimination with quantum coherence

Sunho Kim, Longsuo Li, Asutosh Kumar, Chunhe Xiong, Junde Wu

Published Jul 12, 2018• 0 citations
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Abstract

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.

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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.
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 is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.
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
We study intrinsic coherence in the tripartite process to unambiguously discriminate two nonorthogonal states of a qubit, entangled with another one, and assisted by an auxiliary system. The optimal success probability is found to be benefited by initial intrinsic coherence, but no extra one is required. The transformations among different contributions of intrinsic coherence are necessary in this procedure, which increase with the overlap between the states to recognize. Such state discrimination is a key step of the probabilistic teleportation protocol. Entanglement of the quantum channel decreases the coherence characterizing the reliance on an ancilla.
Generalized contextuality is known to be required in optimal strategies for quantum state discrimination protocols. More recently, sequential discrimination tasks have been studied; n players attempt to determine in which state a qubit was prepared, in such a way that they all have a finite probability of success. We consider the extent to which contextuality plays a role in sequential versions of both unambiguous and minimum error discrimination. In the standard nonsequential case where n = 1, we use the COPE formalism to demonstrate that the presence of contextuality is guaranteed not only for the optimal measurement, but for a specific set of nonoptimal measurements as well. In the sequential case n > 1, we show that the presence of contextuality depends on which states are prepared, and on the protocol (unambiguous or minimum error) selected.