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Chinese Physics Letters

Efficient Three-Party Quantum Secret Sharing with Single Photons

Ping Zhou, Xihan Li, Deng Fu-Guo, Hong-Yu Zhou

Published Jul 26, 2007• 26 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/24/8/008

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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.
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.
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 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 quantum secret sharing (QSS) scheme with single photons was proposed, the trusted third party (TTP) encoded the secret value into conjugate single quantum states, in the revealing phase each participant performs the corresponding unitary operation on the single photon sequence sequentially according to its’ private key, and the participants can recover the secret value only through one round of interaction with the TTP and two round of interactions between themselves, further more any dishonest action and malicious attack can be detected.
A circular quantum secret sharing protocol is proposed, which is useful and efficient when one of the parties of secret sharing is remote to the others who are in adjacent, especially the parties are more than three. We describe the process of this protocol and discuss its security when the quantum information carrying is polarized single photons running circularly. It will be shown that entanglement is not necessary for quantum secret sharing. Moreover, the theoretic efficiency is improved to approach 100% as almost all the instances can be used for generating the private key, and each photon can carry one bit of information without quantum storage. It is straightforwardly to utilize this topological structure to complete quantum secret sharing with multi-level two-particle entanglement in high capacity securely.
Most semi-quantum secret sharing protocols are suitable for the application with three participants. Based on the n-level states, a multiparty semi-quantum secret sharing protocol is proposed. Compared with similar protocols, it has the merits as follows. (1) The dealer only needs to prepare the single photon sequence without using any product state or entangle state. (2) To share a secret, the classical parties need not have the ability of measurement. They only need to reorder the photon sequence and send it to the receiver. (3) The dealer knows nothing about any agent’s secret shadow. Therefore, it is infeasible for the dealer to impersonate the classical participant to pool the secret shadow during the secret recovering phase. (4) Theoretically, the qubit efficiency of the proposed protocol is asymptotically 100%. The protocol is secure against famous attacks such as intercept-resend attack, measurement-resend attack and entangle-measure attack.