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Chinese Physics Letters

Explicit Protocol for Deterministic Entanglement Concentration

Gu Yong-Jian, Peng Gao, Guo Guang-Can

Published Jun 16, 2005• 4 citations
Publisher

Abstract

We present an explicit protocol for extraction of an EPR pair from two partially entangled pairs in a deterministic fashion via local operations and classical communication. This protocol is constituted by a local measurement described by a positive operator-valued measure (POVM), one-way classical communication, and a corresponding local unitary operation or a choice between the two pairs. We explicitly construct the required POVM by the analysis of the doubly stochastic matrix connecting the initial and the final states. Our scheme might be useful in future quantum communication.

DOI
10.1088/0256-307x/22/7/009

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We present an explicit protocol for extraction of an EPR pair from two partially entangled pairs in a deterministic fashion via local operations and classical communication. This protocol is constituted by a local measurement described by a positive operator-valued measure (POVM), one-way classical communication, and a corresponding local unitary operation or a choice between the two pairs. We explicitly construct the required POVM by the analysis of the doubly stochastic matrix connecting the initial and the final states. Our scheme might be useful in future quantum communication.
Entanglement concentration can be achieved in a deterministic fashion [Morikoshi, Phys. Rev. Lett. 84, 3189 (2000); Phys. Rev. A 64, 022316 (2001)]. We present a protocol for deterministic extraction of an Einstein-Podolsky-Rosen pair from two partially entangled pairs via local operations and classical communication. This protocol consists of a generalized measurement described by a positive operator-valued measure (POVM), one-way classical communication, and a corresponding unitary operation or a choice between the two pairs. Based on the theory of majorization, we explicitly construct the required POVM, which can be realized by performing a unitary operation in the extended space and a conventional Von Neuman orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the deterministic entanglement concentration. Our method for constructing quantum circuits differs from the usual method based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.
According to the Nielsens theorem and the basic idea of entanglement concentration, we improve and extend the deterministic entanglement concentration protocol that extracts one pair of maximally entangled particles out of two pairs of non-maximally entangled particles, thus establishing a deterministic entanglement concentration protocol that extracts two pairs of maximally entangled particles out of three pairs of non-maximally entangled particles in the way of the classical communication and local operation and the specific positive operator-valued measure. This is helpful for establishing a deterministic entanglement concentration protocol that extracts k pairs of maximally entangled particles out of n pairs of non-maximally entangled particles.
Deterministic extraction of Bell pairs from a finite number of partially entangled pairs is discussed. We derive the maximum number of Bell pairs that can be obtained with probability 1 by local operations and classical communication. It is proved that the optimal deterministic concentration needs only a two-pair collective manipulation in each step, and that a collective manipulation of all entangled pairs is not necessary. Finally, this scheme reveals an entanglement measure for the deterministic concentration.
A deterministic direct quantum communication protocol by using swapping quantum entanglement and local unitary operations is proposed in this paper. A set of ordered EPR pairs in one of the four Bell states is used. For each pair, each of the two legitimate users owns a photon of the entangled pair via quantum channel. The pairs are divided into two types of group, i.e., the checking groups and the encoding-decoding groups. In the checking groups, taking advantage of the swapping quantum entanglement and Alice's (the message sender's) public announcement, the eavesdropping can be detected provided that the number of the checking groups is big enough. After insuring the security of the quantum channel, Alice encodes her bits via the local unitary operations on the encoding-decoding groups. Then she performs her Bell measurements on her photons and publicly announces her measurement results. After her announcement, the message receiver Bob performs his Bell measurements on his photons and directly extracts the encoding bits by using the property of the quantum entanglement swapping. The security of the present scheme is also discussed: under the attack scenarios to our best knowledge, the scheme is secure.
Two schemes for quantum secure conditional direct communication are proposed, where a set of EPR pairs of maximally entangled particles in Bell states, initially made by the supervisor Charlie, but shared by the sender Alice and the receiver Bob, functions as quantum information channels for faithful transmission. After insuring the security of the quantum channel and obtaining the permission of Charlie (i.e., Charlie is trustworthy and cooperative, which means the "conditional" in the two schemes), Alice and Bob begin their private communication under the control of Charlie. In the first scheme, Alice transmits secret message to Bob in a deterministic manner with the help of Charlie by means of Alice's local unitary transformations, both Alice and Bob's local measurements, and both of Alice and Charlie's public classical communication. In the second scheme, the secure communication between Alice and Bob can be achieved via public classical communication of Charlie and Alice, and the local measurements of both Alice and Bob. The common feature of these protocols is that the communications between two communication parties Alice and Bob depend on the agreement of the third side Charlie. Moreover, transmitting one bit secret message, the sender Alice only needs to apply a local operation on her one qubit and send one bit classical information. We also show that the two schemes are completely secure if quantum channels are perfect.