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arXiv:1401.0899 · Europhysics Letters (EPL)

Assisted optimal state discrimination without entanglement

L. F. Xu, F. L. Zhang, M. L. Liang, J. L. Chen

Published Jun 1, 2014• 9 citations
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Abstract

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 $d$ 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.

DOI
10.1209/0295-5075/106/50004

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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.
The roles of quantum correlations, entanglement, discord, and dissonance needed for performing unambiguous quantum state discrimination assisted by an auxiliary system are studied. In general, this procedure for conclusive recognition between two nonorthogonal states relies on the availability of entanglement and discord. However, we find that there exist special cases for which the procedure can be successfully achieved without entanglement. In particular, we show that the optimal case for discriminating between two nonorthogonal states prepared with equal a priori probabilities does not require entanglement but quantum dissonance only.
A fundamental problem in quantum information is to explore what kind of quantum correlations is responsible for successful completion of a quantum information procedure. Here we study the roles of entanglement, discord, and dissonance needed for optimal quantum state discrimination when the latter is assisted with an auxiliary system. In such process, we present a more general joint unitary transformation than the existing results. The quantum entanglement between a principal qubit and an ancilla is found to be completely unnecessary, as it can be set to zero in the arbitrary case by adjusting the parameters in the general unitary without affecting the success probability. This result also shows that it is quantum dissonance that plays as a key role in assisted optimal state discrimination and not quantum entanglement. A necessary criterion for the necessity of quantum dissonance based on the linear entropy is also presented. PACS numbers: 03.65.Ta, 03.67.Mn, 42.50.Dv.
It is shown that the dissonance, a quantum correlation which is equal to quantum discord for separable state, is required for assisted optimal state discrimination. We find that only one side discord is required in the optimal process of assisted state discrimination, while another side discord and entanglement is not necessary. We confirm that the quantum discord, which is asymmetric depending on local measurements, is a resource for assisted state discrimination. With the absence of entanglement, we give the necessary and sufficient condition for vanishing one side discord in assisted state discrimination for a class of ddd nonorthogonal states. As a by-product, we find that the positive-partial-transposition condition is the necessary and sufficient condition for the separability of a class of $2\ifmmode\times\else\texttimes\fi{}d$ states.
We study the procedure for sequential unambiguous state discrimination. A qubit is prepared in one of two possible states and measured by two observers Bob and Charlie sequentially. A necessary condition for the state to be unambiguously discriminated by Charlie is the absence of entanglement between the principal qubit, prepared by Alice, and Bob's auxiliary system. In general, the procedure for both Bob and Charlie to recognize between two nonorthogonal states conclusively relies on the availability of quantum discord which is precisely the quantum dissonance when the entanglement is absent. In Bob's measurement, the left discord is positively correlated with the information extracted by Bob, and the right discord enhances the information left to Charlie. When their product achieves its maximum the probability for both Bob and Charlie to identify the state achieves its optimal value.
Entanglement-assisted discrimination of orthogonal quantum states exhibiting quantum nonlocality is a frontier topic in quantum information theory. In this paper, we investigate the role of multipartite entanglement and develop resource-efficient LOCC discrimination protocols for nonlocal sets of orthogonal states, including multipartite orthogonal product-state sets and entangled-state sets with different nonlocal features. By incorporating controlled-NOT (CNOT) operations into the discrimination procedure, we construct protocols for genuinely nonlocal GHZ bases in four- and five-qubit systems that require only a single EPR pair. For the same target sets, we compare different entanglement-assisted schemes and identify those with lower entanglement consumption. We further observe that, on average, protocols avoiding teleportation consume fewer resources than teleportation-based approaches. In addition, when higher-partite GHZ-type resources (with n>3n>3n>3) are available among suitable subsystems, they can in some cases reduce the overall entanglement cost. Our results highlight the operational significance of multipartite entanglement and provide practical protocols for the local discrimination of orthogonal state sets exhibiting quantum nonlocality.
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