International Journal of Quantum Information

Random numbers (RNs) have applications in many areas: lottery games, gambling, computer simulation, and, most importantly, cryptography [N. Gisin et al., Rev. Mod. Phys. 74 (2002) 145]. In cryptography theory, the theoretical security of the system calls for high quality RNs. Therefore, developing methods for producing unpredictable RNs with adequate speed is an attractive topic. Early on, despite the lack of theoretical support, pseudo RNs generated by algorithmic methods performed well and satisfied reasonable statistical requirements. However, as implemented, those pseudorandom sequences were completely determined by mathematical formulas and initial seeds, which cannot introduce extra entropy or information. In these cases, “random” bits are generated that are not at all random. Physical random number generators (RNGs), which, in contrast to algorithmic methods, are based on unpredictable physical random phenomena, have attracted considerable research interest. However, the way that we extract random bits from those physical entropy sources has a large influence on the efficiency and performance of the system. In this manuscript, we will review and discuss several randomness extraction schemes that are based on radiation or photon arrival times. We analyze the robustness, post-processing requirements and, in particular, the extraction efficiency of those methods to aid in the construction of efficient, compact and robust physical RNG systems.

In this paper, an extended negativity entanglement measure for multipartite k-nonseparable states with respect to k-partition was proposed. We show that this measure is well-defined, i.e. it satisfies some basic properties as an entanglement measure. In addition, we give a relation between this measure and k-ME concurrence, and obtain a lower bound of this measure.

Quantum key distribution (QKD) has been growing rapidly in recent years and becomes one of the hottest issues in quantum information science. During the implementation of QKD on a network, identity authentication has been one main problem. In this paper, an efficient authenticated multi-user quantum key distribution (MQKD) protocol with single particles is proposed. In this protocol, any two users on a quantum network can perform mutual authentication and share a secure session key with the assistance of a semi-honest center. Meanwhile, the particles, which are used as quantum information carriers, are not required to be stored, therefore the proposed protocol is feasible with current technology. Finally, security analysis shows that this protocol is secure in theory.

In this paper, we put forward two novel schemes for probabilistic remote preparation of an arbitrary quantum state with the aid of appropriate local unitary operations when the sender and the receiver only have partial information of non-maximally entangled state, respectively. The concrete implementation procedures of the novel proposals are given in detail. Additionally, the physical realizations of our proposals are discussed based on the linear optics. Because of that neither the sender nor the receiver need to know fully the information of the partially entangled state, our schemes are useful to not only expand the application range of quantum entanglement, but also enlarge the research field of probabilistic remote state preparation (RSP).

In this paper, we quantify the amount of entanglement of bipartite mixed states represented by a statistical mixture of the more general type of two-qubit non-orthogonal states of the form: $|{\psi }_i〉=u_i|{\chi }_i〉\otimes |{\eta }_i〉+v_i|{\chi }_i〉\otimes |{\eta }_i^{\prime }〉+w_i|{\chi }_i^{\prime }〉\otimes |{\eta }_i〉+z_i|{\chi }_i^{\prime }〉\otimes |{\eta }_i^{\prime }〉$, constructed by linearly independent spin coherent states. We use the concurrence as a measure of entanglement and we study its behavior in terms of the amplitudes of SU(2) coherent states.

Quantum phase estimation algorithm (PEA) has been successfully adapted as a sub frame of many other algorithms applied to a wide variety of applications in different fields. However, the requirement of a good approximate eigenvector given as an input to the algorithm hinders the application of the algorithm to the problems where we do not have any prior knowledge about the eigenvector. In this paper, we show that the principal eigenvalue of an irreducible non-negative operator can be determined by using an equal superposition initial state in the PEA. This removes the necessity of the existence of an initial good approximate eigenvector. Moreover, we show that the success probability of the algorithm is related to the closeness of the operator to a stochastic matrix. Therefore, we draw an estimate for the success probability by using the variance of the column sums of the operator. This provides a priori information which can be used to know the success probability of the algorithm beforehand for the non-negative matrices and apply the algorithm only in cases when the estimated probability is reasonably high. Finally, we discuss the possible applications and show the results for random symmetric matrices and 3-local Hamiltonians with non-negative off-diagonal elements.

Based on four-particle GHZ states, the double CNOT operation and the delayed measurement technique, a two-party quantum key agreement (QKA) protocols is proposed. The double CNOT operation makes each four-particle GHZ state collapse into two independent quantum states without any entanglement. Furthermore, one party can directly know the two quantum states and the other party can be aware of the two quantum states by using the corresponding measurement. According to the initial states of the two quantum states, two parties can extract the secret keys of each other by using the publicly announced value or by performing the delayed measurement, respectively. Then the protocol achieves the fair establishment of a shared key. The security analysis shows that the new protocol can resist against participant attacks, the Trojan horse attacks and other outsider attacks. Furthermore, the new protocol also has no information leakage problem and has high qubit efficiency.

In this paper, we study the structure of cyclic, quasi-cyclic codes and their skew codes over the finite ring $B_r=F_2+v_1{F}_2+\cdots +v_r{F}_2$, $v_i^2=v_i,v_i{v}_j=v_j{v}_i=0,1\le i,j\le r$ for $r\ge 1$. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic codes over $B_r$ are obtained. A necessary and sufficient condition for cyclic code over $B_r$ that contains its dual has been given. The parameters of quantum error correcting codes are obtained from cyclic codes over $B_r$.