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arXiv:0906.2555

Two-qubit state sharing between N parties using only Bell pairs and Bell-measurement

Razieh Annabestani, Vahid Karimipour

Published Jun 14, 2009• 0 citations
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Abstract

A quantum protocol for sharing an arbitrary two-qubit state between N parties is introduced. Any of the members, can retrieve the state, only with collaboration of the other parties. We will show that in terms of resources, i.e. the number of classical bits, the number of Bell pairs shared, and also the type of measurements, our protocol is more efficient. For achieving this, we introduce the basic technique of secure passing of an unknown two qubit state among a sequence of parties, none of which can retrieve the state without authorization of the sender and the other members of the group.

DOI
10.48550/arxiv.0906.2555

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We propose a quantum secret sharing protocol between multiparty (mmm members in group 1) and multiparty (nnn members in group 2) using a sequence of single photons. These single photons are used directly to encode classical information in a quantum secret sharing process. In this protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations; then, the last one (the mthm\mathrm{th}mth member of group 1) sends 1∕n1∕n1∕n of the resulting qubits to each of group 2. Thus the secret message shared by all members of group 1 is shared by all members of group 2 in such a way that no subset of each group is efficient to read the secret message, but the entire set (not only group 1 but also group 2) is. We also show that it is unconditionally secure. This protocol is feasible with present-day techniques.
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We present an efficient scheme for sharing an arbitrary m-qubit state with n agents. In our scheme, the sender Alice first shares m Bell states with the agent Bob, who is designated to recover the original m-qubit state. Furthermore, Alice introduces n − 1 auxiliary particles in the initial state |0⟩, applies Hadamard (H) gate and Controlled-Not (CNOT) gate operations on the particles, which make them entangled with one of m particle pairs in Bell states, and then sends them to the controllers (i.e., other n − 1 agents), where each controller only holds one particle in hand. After Alice performing m Bell-basis measurements and each controller a single-particle measurement, the recover Bob can obtain the original unknown quantum state by applying the corresponding local unitary operations on his particles. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.
Quantum secret sharing (QSS), an important branch of quantum communication, is the generalization of classical secret sharing into quantum scenario. The secret messages are split into several parts, and each part is distributed to a separate party so that no action of a subset of all the parties without the cooperation of the entire group is able to read out the secret messages. In this paper, a quantum state sharing protocol is proposed by using entanglement swapping and random EPR selection. The EPR pairs of Bell-state measurement are selected randomly by the sender Alice, which can improve the security of the scheme and raise probability of detecting Eve to 95.8%. In addition, difference coding is used in this protocol to achieve a high efficiency. The security of the present multiparty QSS against eavesdropping has been analyzed. It is convenient in application as it require only two qubit entanglements, one measuring-basis and two-qubit joint measurements, not GHZ states, for sharing an arbitrary secret two-qubit state.
A quantum authentication protocol is presented in this paper. It is based on the correlations of the EPR(Einstain- Podolski-Rosen) pair which is a two-qubit system in one of the four Bell states. The two parties share a sequence of EPR pairs as the authentication key. To authenticate each other, they need to create auxiliary particles and make them interact with the authentication key. Then one can affirm the other's identity by performing the Bell states measure- ment. No one without the authentication key can pass the authentication process. So the protocol is secure. No clas- sical channel and classical information exchange is needed in the authentication process. After the authentication pro- cess, the authentication key can be turned into the origin state. So the authentication key can be reused.