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arXiv:quant-ph/0101066 · Journal of Physics A Mathematical and General

Secure communication with single-photon two-qubit states

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

Published Jul 5, 2002• 127 citations

Abstract

We propose a cryptographic scheme that is deterministic: Alice sends single photons to Bob, and each and every photon detected supplies one key bit—no photon is wasted. This is in marked contrast to other schemes in which a random process decides whether the next photon sent will contribute to the key or not. The determinism is achieved by preparing the photons in two-qubit states, rather than the one-qubit states used in conventional schemes. In particular, we consider the realistic situation in which one qubit is the photon polarization and the other a spatial alternative. Further, we show how one can exploit the deterministic nature for direct secure communication, that is without the need for establishing a shared key first.

DOI: 10.1088/0305-4470/35/28/103

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A scheme for three-party quantum secret sharing of a private key is presented with single photons. The agent Bob first prepares a sequence of single photons with two biased bases and then sends them to the boss Alice who checks the security of the transmission with measurements and produces some decoy photons by rearranging the orders of some sample photons. Alice encodes her bits with two unitary operations on the photons and then sends them to the other agent. The security of this scheme is equivalent to that in the modified Bennett–Brassard 1984 quantum key distribution protocol. Moreover, each photon can carry one bit of the private key and the intrinsic efficiency for qubits and the total efficiency both approach the maximal value 100% when the number of the bits in the key is very large.

In a deterministic quantum key distribution (DQKD) protocol with a two-way quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the qubit and sends it back to Bob. After measuring the returned qubit, Bob can obtain Alice's key bit immediately, without basis reconciliation. Since an eavesdropper may attack the qubits traveling on either the Bob-Alice channel or the Alice-Bob channel, the security analysis of DQKD protocol with a two-way quantum channel is complicated and its unconditional security has been controversial. This paper presents a security proof of a single-photon four-state DQKD protocol against general attacks.

We propose a scheme of quantum secret sharing between Alice's group and Bob's group with single photons and unitary transformations. In the protocol, one member in Alice's group prepares a sequence of single photons in one of four different states, while other members directly encode their information on the sequence of single photons via unitary operations; after that, the last member sends the sequence of single photons to Bob's group. Then Bob's, except for the last one, do work similarly. Finally the last member in Bob's group measures the qubits. If the security of the quantum channel is guaranteed by some tests, then the qubit states sent by the last member of Alice's group can be used as key bits for secret sharing. It is shown that this scheme is safe.