Since the first quantum secret sharing protocol based on Greenberger–Horne–Zeilinger (GHZ) states was presented by Hillery et al, dozens of quantum secret sharing protocols based on different entangled states (e.g. Bell states, d-level Bell states and GHZ states, etc) and product states have been developed. In this paper, we present a quantum secret sharing protocol, in which the genuinely maximally entangled six-qubit states, which was found recently by Borras et al, are used. An ordinary entangled state such as a Bell state or a GHZ state, etc can be used to share at most only one bit. However, according to our protocol, Alice can share three bits among three parties by a six-qubit state, which shows that our protocol is more efficient than any previous protocol.
A large payload bidirectional quantum secure direct communication (BQSDC) protocol without information leakage is proposed, which is based on entanglement swapping between any two Greenberger–Horne–Zeilinger (GHZ) states. Two remote authorized parties, Alice and Bob, can safely exchange their individual secret messages without worrying about the information leakage problem. Our protocol uses a shared secret GHZ state to overcome the information leakage problem. The shared secret GHZ state plays two roles in the bidirectional communication process: on one hand, it lets Bob know the prepared initial state; on the other hand, it is used for encoding Bob's secret messages. Moreover, our protocol can transmit six bits of secret messages per round communication. Compared with those previous BQSDC protocols, the advantage of our protocol lies in having the following two characters simultaneously: on one hand, it overcomes the information leakage problem; one the other hand, its capacity is as high as six bits per round communication.
We initiate the study of quantum leakage resilience of unmodified Shamir secret sharing over prime fields. A well-studied leakage model for Shamir's secret sharing classically is single-bit local leakage from each share. We consider its quantum analogue where, for each party, a local leakage channel takes as input the party's share and outputs a leaked qubit. Without preshared entanglement, we show that the distinguishing advantage is
2−Ω(n) when the threshold rate
t/n=τ exceeds
τ⋆≈0.73339 by a fixed positive margin.
More generally, we allow disjoint entangled blocks of any fixed maximum size where there is no entanglement between different blocks or with the adversary, and each block emits at most a fixed number of qubits. Security holds when the threshold rate is high enough (sufficiently close to one). We then allow a specified set of devices to share entanglement with the adversary. We show that security holds even when a linear number of devices (
αn for small
α>0) share entanglement with each other and with the adversary for a large enough threshold rate.
As a complementary negative result, we also show that even classical single-bit leakage makes Shamir scheme insecure if we allow arbitrarily large entanglement between the leakage devices. A GHZ state shared by exactly
t leakage devices makes even classical one-bit leakage insecure, without any entanglement with the adversary. In this attack, each participating device emits only one classical bit, and their joint parity distinguishes any chosen pair of secrets with a constant advantage. Thus, for fixed threshold rates above
τ⋆, the maximum number of devices that may share arbitrary entanglement with one another and with the adversary while preserving security is linear in
n up to constant factors, although the optimal support fraction remains open.
Entanglement is an important resource which can be applied in quantum information processing. Now, Bell states and GHZ states have been widely used in quantum secret sharing. The genuinely maximally entangled six-qubit state, which was discovered by Borras recently and called as Borras state, has been shown to exhibit some excellent characters in quantum teleportation. By analyzing the structure of Borras state and making generalized Schmidt decomposition, this paper constructs a concrete protocol of quantum secret sharing, in which Alice can share two bits among her agents, if she shares a Borras state with her four agents in advance (each agent has one qubit, and Alice has two qubits).