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Computational matematics series/Computational mathematics series

Communicating with qubit pairs

Almut Beige, Berthold‐Georg Englert, Christian Kurtsiefer, Harald Weinfurter

Published Feb 14, 2002• 1 citation
Publisher
DOI
10.1201/9781420035377.pt8

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We analyze the amount of classical communication required to reproduce the statistics of local projective measurements on a general pair of entangled qubits, |ΨAB⟩=p |00⟩+1−p |11⟩ (with 1/2≤p≤1 ). We construct a classical protocol that perfectly simulates local projective measurements on all entangled qubit pairs by communicating one classical trit. Additionally, when 2p(1−p)2p−1log⁡(p1−p)+2(1−p)≤1 , approximately 0.835≤p≤1 , we present a classical protocol that requires only a single bit of communication. The latter model even allows a perfect classical simulation with an average communication cost that approaches zero in the limit where the degree of entanglement approaches zero ( p→1 ). This proves that the communication cost for simulating weakly entangled qubit pairs is strictly smaller than for the maximally entangled one.
In this paper, we present a multi-partner communication network protocol. The supervisor prepares numerous Einstein–Podolsky–Rosen (EPR) pairs and auxiliary qubits. He then performs a controlled-NOT(CNOT) gate operation on one qubit of each EPR pair and an auxiliary, which induces the entanglement between the EPR pair and the auxiliary. The supervisor keeps one qubit sequence in his laboratory and sends the others to the outside world. After security approval, the network can be constructed successfully, which can be applied to quantum secret sharing and quantum secure direct communication.
In this paper, we propose a quantum secure direct communication (QSDC) network architecture based on EPR pairs. This network architecture can implement quantum secure direct communication with intermediate nodes. In this QSDC network architecture, there are several server nodes which are connected with quantum channels and classical channels. An authentication server is used to identify users. The server nodes can generate EPR pairs and deliver the qubits through the quantum channel to the other node. We also propose a QSDC protocol. The users request to share constant number of EPR pairs with the nearest server nodes. The server nodes teleport the sender's qubits to the receiver. The sender can transmit arbitrary number of qubits to the receiver.