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Chinese Physics Letters

Fault-Tolerate Three-Party Quantum Secret Sharing over a Collective-Noise Channel

Chunyan Li, Yansong Li

Published Feb 1, 2011• 13 citations
Publisher

Abstract

We present a fault-tolerate three-party quantum secret sharing (QSS) scheme over a collective-noise channel. Decoherence-free subspaces are used to tolerate two noise modes, a collective-dephasing channel and a collective-rotating channel, respectively. In this scheme, the boss uses two physical qubits to construct a logical qubit which acts as a quantum channel to transmit one bit information to her two agents. The agents can get the information of the private key established by the boss only if they collaborate. The boss Alice encodes information with two unitary operations. Only single-photon measurements are required to rebuilt Alice's information and detect the security by the agents Bob and Charlie, not Bell-state measurements. Moreover, Almost all of the photons are used to distribute information, and its success efficiency approaches 100% in theory.

DOI
10.1088/0256-307x/28/2/020304

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We present a fault-tolerate three-party quantum secret sharing (QSS) scheme over a collective-noise channel. Decoherence-free subspaces are used to tolerate two noise modes, a collective-dephasing channel and a collective-rotating channel, respectively. In this scheme, the boss uses two physical qubits to construct a logical qubit which acts as a quantum channel to transmit one bit information to her two agents. The agents can get the information of the private key established by the boss only if they collaborate. The boss Alice encodes information with two unitary operations. Only single-photon measurements are required to rebuilt Alice's information and detect the security by the agents Bob and Charlie, not Bell-state measurements. Moreover, Almost all of the photons are used to distribute information, and its success efficiency approaches 100% in theory.
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 this paper,two fault tolerant channel-encrypting quantum dialogue(QD)protocols against collective noise are presented.One is against collective-dephasing noise,while the other is against collective-rotation noise.The decoherent-free states,each of which is composed of two physical qubits,act as traveling states combating collective noise.Einstein-Podolsky-Rosen pairs,which play the role of private quantum key,are securely shared between two participants over a collective-noise channel in advance.Through encryption and decryption with private quantum key,the initial state of each traveling two-photon logical qubit is privately shared between two participants.Due to quantum encryption sharing of the initial state of each traveling logical qubit,the issue of information leakage is overcome.The private quantum key can be repeatedly used after rotation as long as the rotation angle is properly chosen,making quantum resource economized.As a result,their information-theoretical efficiency is nearly up to 66.7%.The proposed QD protocols only need single-photon measurements rather than two-photon joint measurements for quantum measurements.Security analysis shows that an eavesdropper cannot obtain anything useful about secret messages during the dialogue process without being discovered.Furthermore,the proposed QD protocols can be implemented with current techniques in experiment.
Based on the quantum key distribution protocol [X. H. Li, F. G. Deng and H. Y. Zhou, Phys. Rev. A78 (2008) 022321], we proposed two efficient fault-tolerant quantum secret sharing schemes over two collective-noise channels, in which the sharers can establish a key with the sender only if all the sharers collaborate together. Noiseless subspaces are composed of two Bell states based on the hypothesis of collective noise and the spatial degree of freedom is introduced to insure the security. Although entangled states are used to encode the key bits, the sharers are only required to perform single-particle product operations or single-particle product measurement, making the schemes convenient with current technique. As there is no basis mismatch during the measurement, almost all of the samples can be used to share the key.
We present two quantum key distribution (QKD) schemes over a collective-noise channel. Each logical qubit, composed of two physical qubits with a decoherence-free subspace, is immune to a collective noise and can carry one bit of information in theory. Although the receiver should prepare entangled two-photon quantum systems, he can read out the information encoded by the sender with two unitary operations on two photons, resorting to only two single-photon measurements, not Bell-state measurements, which makes these protocols simpler than others in experiment. These two QKD protocols are deterministic, not random, which makes the classical information exchanged be reduced largely. Also, they have a high intrinsic efficiency.
This paper presents a scheme for high-capacity three-party quantum secret sharing with quantum superdense coding, following some ideas in the work by Liu et al (2002 Phys. Rev. A 65 022304) and the quantum secret sharing scheme by Deng et al (2008 Phys. Lett. A 372 1957). Instead of using two sets of nonorthogonal states, the boss Alice needs only to prepare a sequence of Einstein–Podolsky–Rosen pairs in d -dimension. The two agents Bob and Charlie encode their information with dense coding unitary operations, and security is checked by inserting decoy photons. The scheme has a high capacity and intrinsic efficiency as each pair can carry 2lb d bits of information, and almost all the pairs can be used for carrying useful information.
We present two robust quantum secret sharing protocols against two kinds of collective noise with single logical qubits. Each logical qubit is encoded in two-qubit noiseless states and so it can function over a quantum channel subjected to a collective noise. The safety of transmission is ensured by nonorthogonality of the noiseless states traveling forward and backward on the quantum channel. Moreover, we construct efficient quantum circuits to implement channel encoding and information encoding by means of primitive operations in quantum computation.