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Science China Physics Mechanics and Astronomy

High-efficiency quantum steganography based on the tensor product of Bell states

Shujiang Xu, Xiu‐Bo Chen, Xinxin Niu, Yixian Yang

Published Jul 23, 2013• 20 citations
Publisher
DOI
10.1007/s11433-013-5151-0

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Quantum steganography is the art of hiding secret information in an insecure quantum channel. Recently, it is proposed a quantum steganography protocol based on the tensor product of Bell states to transmit classical 4-bit secret message per round. However, it has permits a small hidden capacity. In this work, an improvement of that quantum steganography protocol to transmit 8-bit secret message per round is proposed. The improved protocol uses tensor product of Bell states and unitary transformations with two groups of sixteen tensor products of two Bell states rather than 256 elements of tensor product of four Bell states. Simulations conducted shows that the improved protocol has superior performance in terms of imperceptibility as well as high security compared with the competitive protocol.
Tensor product operators on finite dimensional Hilbert spaces are studied. The focus is on bilinear tensor product operators. A tensor product operator on a pair of Hilbert spaces is a maximally general bilinear operator into a target Hilbert space. By 'maximally general' is meant every bilinear operator from the same pair of spaces to any Hilbert space factors into the composition of the tensor product operator with a uniquely determined linear mapping on the target space. There are multiple distinct tensor product operators of the same type; there is no "the" tensor product. Distinctly different tensor product operators can be associated with different parts of a multipartite system without difficulty. Separability of states, and locality of operators and observables is tensor product operator dependent. The same state in the target state space can be inseparable with respect to one tensor product operator but separable with respect to another, and no tensor product operator is distinguished relative to the others; the unitary operator used to construct a Bell state from a pair of |0>'s being highly tensor product operator-dependent is a prime example. The relationship between two tensor product operators of the same type is given by composition with a unitary operator. There is an equivalence between change of tensor product operator and change of basis in the target space. Among the gains from change of tensor product operator is the localization of some nonlocal operators as well as separability of inseparable states. Examples are given.