Yimin Liu

Deterministic single-qubit operation sharing with five-qubit cluster state

Perfect sharing of arbitrary single-qubit operation (PSASQO) with shared entanglements and LOCC is focused. A symmetric three-party PSASQO scheme is put forward by utilizing the five-qubit cluster state proposed by Briegel and Raussendorf (Phys Rev Lett 86:910, 2001). Some concrete discussions on the scheme are made, including its important features, the essential role of the quantum channel, its direct generalization to more-party cases, the problem of entanglement structure and its application perspective in some peculiar quantum scenario as well as its security analysis. Particularly, the experimental feasibilities of the scheme and its generalizations are demonstrated, i.e., showing the employed unitary operations are local and accessible single-qubit Pauli and two-qubit control NOT operations according to nowaday experimental techniques.

Quantum operation sharing with symmetric and asymmetric W states

Two tripartite schemes for sharing a single-qubit operation on a remote target state are proposed with symmetric and asymmetric W states, respectively. They are treated and compared from the aspects of quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that the first scheme is better than the second one. In particular, the sharing can be achieved probabilistically with the first scheme while deterministically with the second one.

Four-party deterministic operation sharing with six-qubit cluster state

An efficient four-party scheme is proposed for remotely sharing an arbitrary single-qubit operation by using a six-qubit cluster state as quantum channel and local operation and classical communication. Some specific discussions are made, including the issues of the scheme determinacy, the sharer symmetry, the scheme security and the essential role of quantum channel as well as the current experimental feasibility.

Tripartite quantum operation sharing with two asymmetric three-qubit W states in five entanglement structures

Tripartite remote sharing of any single-qubit operation with two asymmetric three-qubit W states is amply treated. Five schemes are put forward with the W states in five different entanglement structures corresponding to five different distributions of two identical qubit trios in three locations. For all schemes, two features about the security and the agent symmetry are analyzed and confirmed. Moreover, resource consumption, necessary-operation complexity, success probability and efficiency are also worked out and compared mutually. For all schemes, quantum resource consumption and necessary-operation complexity are same. The last scheme needs to cost two additional classical bits than the former four schemes. Nonetheless, the last scheme is deterministic and has the highest efficiency in contrast to the other four probabilistic schemes with lower efficiencies. Through some analyses, it is found that both success probability and intrinsic efficiency of each scheme are completely determined by the corresponding entanglement structure of the two W states. The underlying physics of this feature is revealed. In addition, the implementation feasibility of all the schemes is analyzed and thus confirmed according to the current experimental techniques.

Quantum correlation swapping

Quantum correlations (QCs), including quantum entanglement and those different, are important quantum resources and have attracted much attention recently. Quantum entanglement swapping as a kernel technique has already been applied to quantum repeaters for successfully generating long-distance shared maximally entangled qubit states. Long-distance shared QCs containing shared entanglements are useful and important for some quantum information processing in future quantum networks. In this paper, the concept of quantum entanglement repeater is extended to that of QC repeater by generalizing quantum entanglement swapping to QC swapping. Specifically, the swapping of QCs in a pair of Werner states through a local bipartite von Neumann measurement is treated. Four different QC measures, i.e., entanglement of formation (William in Phys Rev Lett 80:2245, 1998), quantum discord (Ollivier and Zurek in Phys Rev Lett 88:017901, 2001), measurement-induced disturbance (MID) (Luo in Phys Rev A 77:022301, 2008) and ameliorated MID (Girolami et al. in J Phys A 44:352002, 2011), are employed to characterize and quantify QCs. Properties and thresholds of all QCs which occur in the swapping process are revealed, and two different phenomena are exposed and explained. It is found that a long-distance shared QC can be generated from two short-distance ones via QC swapping indeed; however, its amount cannot exceed the minimum one among the QCs in the two initial states and in the measuring state as far as the four quantifiers are concerned.

Quantum identity authentication based on ping-pong technique without entanglements

A quantum identity authentication scheme based on ping-pong technique without entanglements is proposed. It can verify the legitimate user’s identity and update the initial authentication key for reuse. The security of the proposed scheme is extensively analyzed and accordingly confirmed in the case of general individual attacks. The present scheme owns high efficiency due to the use of single-particle states in a two-way quantum channel. Moreover, the scheme is economical and feasible with present-day technique.

Shared quantum control via sharing operation on remote single qutrit

Two qubit-operation-sharing schemes (Zhang and Cheung in J. Phys. B 44:165508, 2011) are generalized to the qutrit ones. Operations to be shared are classified into three different classes in terms of different probabilities (i.e, 1/3, 2/3 and 1). For the latter two classes, ten and three restricted sets of operations are found out, respectively. Moreover, the two generalized schemes are amply compared from four aspects, namely, quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the second scheme is overall more optimal than the first one as far as three restricted sets of operations are concerned. Moreover, the experimental feasibility of our schemes is confirmed with respect to the nowaday technique.

Analytic expressions of quantum correlations in qutrit Werner states

Quantum correlations in qutrit Werner states are extensively investigated with five popular methods, namely, original quantum discord (OQD) (Ollivier and Zurek in Phys Rev Lett 88:017901, 2001), measurement-induced disturbance (MID) (Luo in Phys Rev A 77:022301, 2008), ameliorated MID (AMID) (Girolami et al. in J Phys A Math Theor 44:352002, 2011), relative entropy (RE) (Modi et al. in Phys Rev Lett 104:080501, 2010) and geometric discord (GD) (Dakić et al. in Phys Rev Lett 105:190502, 2010). Two different analytic expressions of quantum correlations are derived. Quantum correlations captured by the former four methods are same and bigger than those obtained via the GD method. Nonetheless, they all qualitatively characterize quantum correlations in the concerned states. Moreover, as same as the qubit case, there exist quantum correlations in separable qutrit Werner states, too.

Analytic expressions of discord and geometric discord in Werner derivatives

Werner derivatives are a special kind of mixing states transformed from Werner states by unitary operations (Hiroshima and Ishizaka in Phys Rev A 62:044302, 2000). In this paper, the inherent quantum correlations in Werner derivatives are quantified by two different quantifiers, i.e., quantum discord and geometric discord. Different analytic expressions of the two discords in Werner derivatives are derived out. Some distinct features of the discords and their underlying physics are exposed via discussions and analyses. Moreover, it is found that the amount of quantum correlations quantified by either quantifier in each derivative cannot exceed that in the original Werner state. In other words, no unitary operation can increase quantum correlation in a Werner state as far as the two quantifiers are concerned.

Analytic expression of quantum correlations in qutrit Werner states undergoing local and nonlocal unitary operations

Quantum correlations of a qutrit pair in Werner states undergoing local and nonlocal unitary operations are quantified in terms of two different methods, i.e., quantum discord (Ollivier and Zurek in Phys Rev Lett 88:017901, 2001) and measurement-induced disturbance (Luo in Phys Rev A 77:022301, 2008). Analytic expressions of the two kinds of quantum correlations in the system are worked on and found to be completely the same. By virtue of investigations and discussions, we expose some distinct features of the correlations and their underlying physics. More importantly, we found that both local and nonlocal unitary operations cannot increase quantum correlation in a qutrit Werner state for the two quantifiers which are concerned.