Quantum secret sharing between <Emphasis Type="Italic">m</Emphasis>-party and <Emphasis Type="Italic">n</Emphasis>-party with six states

A quantum secret sharing scheme between an m-party group and an n-party group is proposed using three conjugate bases. A sequence of single photons, each of which is prepared in one of the six states, is used directly to encode classical information in the quantum secret sharing process. In this scheme, each of all m members in group 1 chooses randomly his/her own secret key individually and independently, and directly encodes his/her respective secret information on the states of single photons via unitary operations, then the last one sends 1/n of the resulting qubits to each member of group 2. By measuring their respective qubits, all members in group 2 share the secret information shared by all members in group 1. It renders impossible a Trojan horse attack with a multi-photon signal, a fake-signal attack with EPR pairs, an attack with single photons, and an attack with invisible photons. We give the upper bounds on the average success probabilities for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states. Supported by the National Natural Science Foundation of China (Grant No. 10671054), the Key Project of Science and Technology Research of Education Ministry of China (Grant No. 207011) and the Natural Science Foundation of Hebei Province, China (Grant Nos. 07M006 and F2009000311)     

Quantum secret sharing based on quantum error-correcting codes

Quantum secret sharing(QSS) is a procedure of sharing classical information or quantum information by using quantum states.This paper presents how to use a [2k-1,1,k] quantum error-correcting code(QECC) to implement a quantum(k,2k 1) threshold scheme.It also takes advantage of classical enhancement of the [2k-1,1,k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously.Because information is encoded into QECC,these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.     

Efficient Three-Party Quantum Dialogue Protocol Based on the Continuous Variable GHZ States

Based on the continuous variable GHZ entangled states, an efficient three-party quantum dialogue protocol is devised, where each legitimate communication party could simultaneously deduce the secret information of the other two parties with perfect efficiency. The security is guaranteed by the correlation of the continuous variable GHZ entangled states and the randomly selected decoy states. Furthermore, the three-party quantum dialogue protocol is directly generalized to an N-party quantum dialogue protocol by using the n-tuple continuous variable GHZ entangled states.     

Analysis of a kind of quantum cryptographic schemes based on secret sharing

Recently, Yang et al. proposed a kind of quantum cryptographic schemes based on secret sharing. The main idea is drawn from the case, where any n participants who share a secret K can co-operate as K does. This process can be applied to encryption, authentication, signature and so on. Unfortunately, since there is no identity authentication of the share’s holder, these schemes inherit the limitation of secret sharing in practice. If some participants do not follow the protocol, the protocol would be a failu...     

On variational expressions for quantum relative entropies

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback–Leibler divergence over projective measurement statistics, is strictly smaller than Umegaki’s quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petz’ conclusion remains true if we allow general positive operator-valued measures. Second, we extend the result to Rényi relative entropies and show that for non-commuting states the sandwiched Rényi relative entropy is strictly larger than the measured Rényi relative entropy for \(\alpha \in (\frac{1}{2}, \infty )\) and strictly smaller for \(\alpha \in [0,\frac{1}{2})\). The latter statement provides counterexamples for the data processing inequality of the sandwiched Rényi relative entropy for \(\alpha < \frac{1}{2}\). Our main tool is a new variational expression for the measured Rényi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive.     

Revisiting Deng et al.’s Multiparty Quantum Secret Sharing Protocol

The multiparty quantum secret sharing protocol [Deng et al. in Chin. Phys. Lett. 23: 1084–1087, 2006] is revisited in this study. It is found that the performance of Deng et al.’s protocol can be much improved by using the techniques of block-transmission and decoy single photons. As a result, the qubit efficiency is improved 2.4 times and only one classical communication, a public discussion, and two quantum communications between each agent and the secret holder are needed rather than n classical communications, n public discussions, and \frac3n2\frac{3n}{2} quantum communications required in the original scheme.     

A Generalized Information Theoretical Model for Quantum Secret Sharing

An information theoretical model for quantum secret sharing was introduced by H. Imai et al. (Quantum Inf. Comput. 5(1), 69–80 2005), which was analyzed by quantum information theory. In this paper, we analyze this information theoretical model using the properties of the quantum access structure. By the analysis we propose a generalized model definition for the quantum secret sharing schemes. In our model, there are more quantum access structures which can be realized by our generalized quantum secret sharing schemes than those of the previous one. In addition, we also analyse two kinds of important quantum access structures to illustrate the existence and rationality for the generalized quantum secret sharing schemes and consider the security of the scheme by simple examples.     

Scheme for sharing classical information via tripartite entangled states

We investigate schemes for quantum secret sharing and quantum dense coding via tripartite entangled states. We present a scheme for sharing classical information via entanglement swapping using two tripartite entangled GHZ states. In order to throw light upon the security affairs of the quantum dense coding protocol, we also suggest a secure quantum dense coding scheme via W state by analogy with the theory of sharing information among involved users.     

基于量子图态的量子秘密共享

本文基于量子图态的几何结构特征,利用生成矩阵分割法,提出了一种量子秘密共享方案.利用量子图态基本物理性质中的稳定子实现信息转移的模式、秘密信息的可扩展性以及新型的组恢复协议,为安全的秘密共享协议提供了多重保障.更重要的是,方案针对生成矩阵的循环周期问题和因某些元素不存在本原元而不能构造生成矩阵的问题提出了有效的解决方案.在该方案中,利用经典信息与量子信息的对应关系提取经典信息,分发者根据矩阵分割理论获得子秘密集,然后将子秘密通过酉操作编码到量子图态中,并分发给参与者,最后依据该文提出的组恢复协议及图态相关理论得到秘密信息.理论分析表明,该方案具有较好的安全性及信息的可扩展性,适用于量子网络通信中的秘密共享,保护秘密数据并防止泄露.     

Quantum Ramp Secret Sharing Scheme and Quantum Operations

In order to improve the efficiency of quantum secret sharing, quantum ramp secret sharing schemes were proposed (Ogawa et al., Phys. Rev. A 72, 032318 [2005]), which had a trade-off between security and coding efficiency. In quantum ramp secret sharing, partial information about the secret is allowed to leak to a set of participants, called an intermediate set, which cannot fully reconstruct the secret. This paper revisits the size of a share in the quantum ramp secret scheme based on a relation between the quantum operations and the coherent information. We also propose an optimal quantum ramp secret sharing scheme.     

Intercept-Resend Attacks on Semi-quantum Secret Sharing and the Improvements

Recently, Li et al. [Phys. Rev. A 82(2):022303, 2010] presented two semi-quantum secret sharing (SQSS) protocols using Greenberger-Horne-Zeilinger-like states. The proposed schemes are quite practical because only the secret dealer needs to be equipped with advanced quantum devices such as quantum memory, whereas the other agents can merely perform classical operations to complete the secret sharing. However, the present study demonstrates the existence of a security pitfall in the eavesdropping check phase of both the schemes, which can lead to an intercept-resend attack and a Trojan horse attack on the two schemes by a dishonest agent, to determine the other agent’s shadow and consequently derive the master key of the SQSS. This contradicts the security requirement of QSS. Fortunately, two possible solutions are proposed herein to eliminate this security pitfall.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

Quantum and Classical Ergotropy from Relative Entropies

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.     

Genuine quantum and classical correlations in multipartite systems

Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the distance between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.     

Comment on “Reply to Comment on?‘Efficient?High-Capacity Quantum Secret Sharing with?Two-Photon Entanglement’?”

In Deng, Li, and Zhou (Phys. Lett. A 373:399, 2009), the authors propose two improved efficient high-capacity quantum secret sharing schemes to solve the problems existed in the Letter (Phys. Lett. A 372:1957, 2008), they claim that these two schemes are secure and efficient. However, we point out here that these two improved schemes are not secure as one agent can obtain all the information without the help from the other agent. We further modify this three-party quantum secret sharing scheme and make it really secure. In the end, we also give a method to generalize our quantum secret sharing scheme to arbitrary multi-party scheme.     

Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p > 1

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn’s Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d ₁,..., d _n ) and (c ₁,..., c _n ) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of several modes. We find that this result implies a solution to the problem of sharing of entanglement in pure Gaussian states and allows for estimating the global entropy of non-Gaussian states based on local measurements. Implications to the actual preparation of multi-mode continuous-variable entangled states are discussed. We compare the findings with the marginal problem for qubits, the solution of which for pure states has a strikingly similar and in fact simple form.     

Efficient multi-party quantum state sharing of an arbitrary two-qubit state

We present an efficient scheme for sharing an arbitrary two-qubit quantum state with n agents. In this scheme, the sender Alice first prepares an n + 2-particle GHZ state and introduces a Controlled-Not (CNOT) gate operation. Then, she utilizes the n + 2-particle entangled state as the quantum resource. After setting up the quantum channel, she performs one Bell-state measurement and another single-particle measurement, rather than two Bell-state measurements. In addition, except that the designated recover of the quantum secret just keeps two particles, almost all agents only hold one particle in their hands respectively, and thus they only need to perform a single-particle measurement on the respective particle with the basis X. Compared with other schemes based on entanglement swapping, our scheme needs less qubits as the quantum resources and exchanges less classical information, and thus obtains higher communication efficiency.     

Member expansion in quantum (t,n) threshold secret sharing schemes

A protocol for member expansion in quantum (t,n) threshold secret sharing schemes was proposed. Without a trusted center and modifying the shares of old participants, the protocol needs that t (t is the threshold) old participants cooperate to generate the new share. Compared with the previous secret sharing protocols, the proposed protocol has the advantage of joining new participants agilely.     

Secure quantum sealed-bid auction with post-confirmation

A new secure quantum auction with post-confirmation is proposed, which is a direct application of the multi-particle super dense coding scheme to the auction problem. In this scheme all bidders use M groups n-particle GHZ states to represent their bids. Different from classical auction protocols and the previous secure quantum sealed-bid auction protocols, in the present scheme, by introducing a post-confirmation mechanism the honesty of the quantum sealed-bid auction is guaranteed, i.e., malicious bidders cannot collude with auctioneers. Also by sharing secret keys with the bidders the auctioneer could insure the anonymity of the bidders.     

Equivalent Definitions of the Quantum Nonadiabatic Entropy Production

The nonadiabatic entropy production is a useful tool for the thermodynamic analysis of continuously dissipating, nonequilibrium steady states. For open quantum systems, two seemingly distinct definitions for the nonadiabatic entropy production have appeared in the literature, one based on the quantum relative entropy and the other based on quantum trajectories. We show that these two formulations are equivalent. Furthermore, this equivalence leads us to a proof of the monotonicity of the quantum relative entropy under a special class of completely-positive, trace-preserving quantum maps, which circumvents difficulties associated with the noncommuntative structure of operators.