Zhan-Jun Zhang

Optimizing resource consumption, operation complexity and efficiency in quantum-state sharing

An original idea is proposed for constructing optimal schemes of quantum-state sharing with respect to resource consumption, operation complexity and efficiency. To elucidate it, a specific tripartite scheme for securely sharing an arbitrary two-qubit quantum information (i.e., a quantum state) is shown. Compared with the three schemes proposed recently (Deng et al 2005 Phys. Rev. A 72 044301, 2006 Eur. Phys. J. D 39 459), the optimal scheme has the distinct advantages of consuming fewer quantum and classical resources, lessening the difficulty and intensity of necessary operations, and having higher intrinsic efficiency.

Shared quantum remote control: quantum operation sharing

We consider three-party sharing of unitary operations with the help of the shared entanglement and LOCC. We propose three separate schemes corresponding to decreasing resource requirements and increasing restrictions on the set of possible operations. It can be shown that our protocols are optimal.

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.

MINIMAL CLASSICAL COMMUNICATION COST AND MEASUREMENT COMPLEXITY IN SPLITTING TWO-QUBIT QUANTUM INFORMATION VIA ASYMMETRIC W STATES

We propose a scheme for splitting a two-qubit quantum information by using two asymmetric W states as quantum channel. In this scheme the split state is assumed to be completely known by the sender. Because of this, during the splitting process, the sender only needs to perform a two-qubit projective measurement. Once the sender announces the measurement result in terms of the prior agreement, then using this message the two receivers can recover the quantum information via their mutual assistance. We calculate the success probability and classical communication cost of the scheme. In general, the splitting success probability (SSP) is 1/4 and the average classical communication cost is 0.25 bit. However, we find that for some states the SSP can reach 0.5 or even unity after consuming a little additional classical resource.

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.

TRIPARTITION OF ARBITRARY SINGLE-QUBIT QUANTUM INFORMATION BY USING ASYMMETRIC FOUR-QUBIT W STATE

In this paper we propose a four-party scheme for a sender to achieve the tripartition of his/her arbitrary single-qubit quantum information among three recipients via an asymmetric four-qubit W state as quantum channels. In the scheme, if and only if, the three recipients cooperate together, they can perfectly retrieve the senders quantum information by performing first two 2-qubit collective unitary operations and then a single-qubit unitary operation. The scheme is symmetric with respect to the reconstruction for any recipient can conclusively recover the quantum information with the other twos helps.

A QUANTUM SPLITTING SCHEME OF ARBITRARY TWO-QUBIT STATE USING FOUR-QUBIT CLUSTER STATE

In this paper, we explore the channel capacity of the 4-qubit 4-term cluster state (i.e. (|0000〉 + |0011〉 + |1100〉 - |1111〉)/2) for splitting arbitrary two-qubit quantum information. After our extensive investigations, we found that 4 out of 12 possible distributions of the 4 qubits can be utilized to realize bipartite splitting. In terms of each distribution, the corresponding splitting scheme is presented and LOCCs (local operation and classical communication) are explicitly given.

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.

GENERALIZED THREE-PARTY QUBIT OPERATION SHARING

Two three-party schemes of qubit operation sharing proposed by Zhang and Cheung [J. Phys. B44 (2011) 165508] are generalized by utilizing partially entangled states as quantum channels instead of maximally entangled ones. Their quantum and classical resource consumptions, necessary-operation complexities, success probabilities and efficiencies are calculated and compared with each other. Moreover, it is revealed that the success probabilities are completely determined by the shared entanglement.