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arXiv:1609.05134 · Europhysics Letters (EPL)

Intrinsic coherence in assisted sub-state discrimination

Fulin Zhang, Teng Wang

Published Jan 1, 2017• 4 citations
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Abstract

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.

DOI
10.1209/0295-5075/117/10013

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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.
A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work [Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of ddd states [Phys. Rev. A, 85 (2012) 022328] have only proved that entanglement can be absent in the case with equal a \emph{priori} probabilities. By improving the protocol in [Sci. Rep., 3 (2013) 2134], we investigate this topic in a simple case to discriminate three nonorthogonal states of a qutrit, with positive real overlaps. In our procedure, the entanglement between the qutrit and an auxiliary qubit is found to be completely unnecessary. This result shows that the quantum dissonance may play as a key role in optimal state discrimination assisted by a qubit for more general cases.
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
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.
Quantum teleportation is of significant meaning in quantum information. We study the probabilistic teleportation of unknown two-qubit entangled state utilizing non-maximally entangled GHZ state as quantum channel. We formulate it as unambiguous state discrimination problem and derive exact optimal POVM operator for maximizing the success probability of unambiguous state discrimination. Only one three-qubit POVM for the sender, one two-qubit unitary operation for the receiver and two cbits for outcome notification are required in this scheme. The unitary operation is given in the form of concise formula and average fidelity is calculated. We show that our scheme is applicable in the situation where the information of quantum channel is only available for the sender.