Deterministic secure communication protocol

Quantum key distribution (QKD) is a protocol which is provably secure, by which private key bit can be created between two parties over a public channel. The key bits can then be used to implement a classical private key cryptosystem, to enable the parties to communicate securely. The basic idea behind QKD is that Eve cannot gain any information from the qubits transmitted from Alice to Bob without disturbing their state. First, the no-cloning theorem forbids Eve to perfectly clone Alice’s qubit. Second, in any attempt to distinguish between two non-orthogonal quantum states, information gain is only possible at the expense of introducing disturbance to the signal [1]. Based on the postulate of quantum measurement [2] and no-cloning theorem [3], different QKD protocols are presented [4-8]. However, these types of cryptographic schemes are usually nondeterministic. Recently, K. Bostrom and T. Felbinger presented a protocol, which allows for deterministic communication using entanglement [9,10]. The basic idea of protocol [9] is that one can encode the information locally on an EPR pair, but it has a nonlocal effect. In this paper, we show a secure communication protocol which is a deterministic secure direct communication protocol using single qubit in mixed state. This protocol is based on the property that non-orthogonal quantum states cannot be reliably distinguished [2]. One cannot simultaneously measure the polarization of a photon in the vertical-horizontal basis and simultaneously in the diagonal basis. It is well known that we can prepare a photon in states {|0 >, |1 >} or {|φ0 >, |φ1 >}in its polarization degree of freedom, where