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International Journal of Quantum Information

Generalized three-party sharing of operations on remote single qutrit

Pengfei Xing, Yimin Liu, Chuanmei Xie, Xiansong Liu, Zhanjun Zhang

Published Apr 1, 2014• 2 citations
Publisher

Abstract

Two three-party schemes are put forward for sharing quantum operations on a remote qutrit with local operation and classical communication as well as shared entanglements. The first scheme uses a two-qutrit and three-qutrit non-maximally entangled states as quantum channels, while the second replaces the three-qutrit non-maximally entangled state with a two-qutrit. Both schemes are treated and compared from the four aspects of quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the latter is overall more optimal than the former as far as a restricted set of operations is concerned. In addition, comparisons of both schemes with other four relevant ones are also made to show their two features, including degree generalization and channel-state generalization. Furthermore, some concrete discussions on both schemes are made to expose their important features of security, symmetry and experimental feasibility. Particularly, it is revealed that the success probabilities and intrinsic efficiencies in both schemes are completely determined by the shared entanglement.

DOI
10.1142/s0219749914500117

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Two three-party schemes are put forward for sharing quantum operations on a remote qutrit with local operation and classical communication as well as shared entanglements. The first scheme uses a two-qutrit and three-qutrit non-maximally entangled states as quantum channels, while the second replaces the three-qutrit non-maximally entangled state with a two-qutrit. Both schemes are treated and compared from the four aspects of quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the latter is overall more optimal than the former as far as a restricted set of operations is concerned. In addition, comparisons of both schemes with other four relevant ones are also made to show their two features, including degree generalization and channel-state generalization. Furthermore, some concrete discussions on both schemes are made to expose their important features of security, symmetry and experimental feasibility. Particularly, it is revealed that the success probabilities and intrinsic efficiencies in both schemes are completely determined by the shared entanglement.
A probabilistic tripartite single-qubit operation sharing scheme is put forward by utilizing a two-qubit and a three-qubit non-maximally entangled state as quantum channels. Some specific comparisons between our scheme and another probabilistic scheme are made. It is found that, if the product of the two minimal coefficients characterizing channel entanglements is greater than 3/16, our scheme is more superior than the other one. Nonetheless, the price is that more classical and quantum resources are consumed, and the operation difficulty is rather increased. Moreover, some important features of the scheme, such as its security, probability and sharer symmetry, are revealed through concrete discussions. Additionally, the experimental feasibility of our scheme is analyzed and subsequently confirmed according to the current experimental techniques.
Two tripartite schemes are put forward with shared entanglements and Local Operation and Classical Communication (LOCC) for sharing an operation on a remote target sate. The first scheme uses a Bell and a symmetric W states as quantum channels, while the second replaces the symmetric W state by an asymmetric one. Both schemes 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 latter scheme is better than the former one. Particularly, the sharing can be achieved only probabilistically with the first scheme deterministically with the second one.
Two tripartite schemes are put forward with shared entanglements and LOCC for sharing an operation on a remote target sate. The first scheme uses a Bell and a symmetric W states as quantum channels, while the second replaces the symmetric W state by an asymmetric one. Both schemes 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 latter scheme is better than the former one. Particularly, the sharing can be achieved only probabilistically with the first scheme deterministically with the second one.
A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed, where two non-maximally-entangled three-qutrit states are taken as the quantum channel among three parties. With the sender's help, if and only if both receivers collaborate together, they can securely share the quantum state in a probabilistic way by introducing an ancilla qutrit and performing appropriate unitary operations. The relation between the success probability and coefficients characterizing the quantum channel is revealed. The security of the present scheme is analyzed and confirmed. Moreover, the generalization of the three-party scheme to more-party case is also sketched.
A four-party single-qubit operation sharing scheme is put forward by utilizing the Bell and Yeo–Chua product state in an entanglement structure as the composite quantum channel. Four features of the scheme are discussed and confirmed, including its determinacy, symmetry, and security as well as the scheme experimental feasibility. Moreover, some concrete comparisons between our present scheme and a previous scheme [H. Xing et al., Quantum Inf. Process. 13 (2014) 1553] are made from the aspects of quantum and classical resource consumption, necessary operation complexity, and intrinsic efficiency. It is found that our present scheme is more superior than that one. In addition, the essential reason why the employed state in the entanglement structure is applicable for sharing an arbitrary single-qubit operation among four parties is revealed via deep analyses. With respect to the essential reason, the capacity of the product state in quantum operation sharing (QOS) is consequently shown by simple presenting the corresponding schemes with the state in other entanglement structures.