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Communications in Theoretical Physics

Accessible Information for Equally-Distant Partially-Entangled Alphabet State Resource

Hao San-Ru, Hou Bo-Yu, Xiao-Qiang Xi, Rui‐Hong Yue

Published Feb 15, 2002• 0 citations

Abstract

We have proposed a quantum system with equally-distant partially-entangled alphabet which has the minimal mutual overlap and the highly distinguishability, these quantum are used as the signal states of the quantum communication. We have also constructed the positive operator-valued measure for these signal states and discussed their entanglement properties and measurement of entanglement. We calculate the accessible information for these alphabet and show that the accessible information is closely related to the entanglement of the signal states: the higher the entanglement of the signal states, the better the accessible information of the quantum system, and the accessible information reaches its maximal value when the alphabet have their maximal entanglement.

DOI: 10.1088/0253-6102/37/2/149

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We have proposed a quantum system with equally-distant partially-entangled alphabet which has the minimal mutual overlap and the highly distinguishability, these quantum are used as the signal states of the quantum communication. We have also constructed the positive operator-valued measure for these signal states and discussed their entanglement properties and measurement of entanglement. We calculate the accessible information for these alphabet and show that the accessible information is closely related to the entanglement of the signal states: the higher the entanglement of the signal states, the better the accessible information of the quantum system, and the accessible information reaches its maximal value when the alphabet have their maximal entanglement.

We exactly evaluate a number of multipartite entanglement measures for a class of graph states, including d -dimensional cluster states ( d = 1,2,3), the Greenberger–Horne–Zeilinger states, and some related mixed states. The entanglement measures that we consider are continuous, 'distance from separable states' measures, including the relative entropy, the so-called geometric measure, and robustness of entanglement. We also show that for our class of graph states these entanglement values give an operational interpretation as the maximal number of graph states distinguishable by local operations and classical communication (LOCC), as well as supplying a tight bound on the fixed letter classical capacity under LOCC decoding.

Entanglement, a weird quantum correlation between separate physical systems, is an indispensable resource for quantum information processing. As with other physical resources, the key to understanding its full potential is to quantify it. In this paper, I review our recent insights into the quantification of entanglement based on the operational notion of accessibility between physical states. In particular, I show that the partially ordered structure of mixed entangled states underlies the non-uniqueness of their entanglement measure.

Each Bell state has the property that by performing just local operations on one qubit, the complete Bell basis can be generated. That is, states generated by local operations are totally distinguishable. This remarkable property is due to maximal quantum entanglement between the two particles. We present a set of local unitary transformations that generate out of partially entangled two-qubit state a set of four maximally distinguishable states that are mutually equally distant. We discuss quantum dense coding based on these alphabet states.

Abstract Entanglement between distant quantum systems is a critical resource for implementing quantum communication. This property is affected by external agents and can be restored by employing efficient entanglement purification protocols. In this work, we propose an entanglement purification protocol based on two entangling two-qubit operations that replace the usual controlled-NOT (CNOT) gate. These operations arise from a generalised quantum measurement and can be understood as measurement operators in a positive operator-valued measure. Furthermore, two variants of the core protocol are introduced and their performances are studied in terms of the overall success probability of reaching a Bell state and the number of purifiable states. Based on rank-two states, we can obtain analytical expressions for the success probability that we extend and refine using numerical calculations to the case of maximally entangled states. We also consider more general rank-three states to show that our procedure is in general more convenient compared to purification protocols based on Bell diagonal states. Finally, we test the protocols using initial random states. In all cases, we find a better performance and a larger amount of purifiable states using our schemes compared to the CNOT-based protocol.