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International Journal of Quantum Information

Deterministic tripartite sharing of eight restricted sets of single-qubit operations with two Bell states or a GHZ state

Hang Xing, Daochu Liu, Pengfei Xing, Chuanmei Xie, Xiansong Liu, Zhanjun Zhang

Published Apr 1, 2014• 15 citations
Publisher

Abstract

Two tripartite schemes with a pair of Bell states and a Greenberger–Horne–Zeilinger (GHZ) state respectively have been proposed recently by Zhang and Cheung for remotely sharing two restricted sets of operations in a deterministic manner [J. Phys. B 44 (2011) 165508]. In this paper, we generalize the schemes with the same quantum channels so that another six restricted sets of operations can be shared deterministically, too. Features about scheme security, sharer symmetry, fulfillment determinacy and experimental feasibility are discussed and revealed. Moreover, some comparisons are also made from the aspects of quantum and classical resource consumption, necessary operation complexity and efficiency.

DOI
10.1142/s0219749914500129

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Two tripartite schemes with a pair of Bell states and a Greenberger–Horne–Zeilinger (GHZ) state respectively have been proposed recently by Zhang and Cheung for remotely sharing two restricted sets of operations in a deterministic manner [J. Phys. B 44 (2011) 165508]. In this paper, we generalize the schemes with the same quantum channels so that another six restricted sets of operations can be shared deterministically, too. Features about scheme security, sharer symmetry, fulfillment determinacy and experimental feasibility are discussed and revealed. Moreover, some comparisons are also made from the aspects of quantum and classical resource consumption, necessary operation complexity and efficiency.
A tripartite operation sharing scheme is put forward by employing a five-qubit entangled state [proposed by Brown et al., J. Phys. A 38, 1119 (2005)] as quantum channel. Its sharer asymmetry and its success determinacy are both identified. Moreover, its security is ensured via analyses. In terms of current techniques, its experimental feasibility is discussed and thus confirmed. Furthermore, its comparison with Ye et al.’s scheme [Chin. Phys. Lett. 30, 020301 (2013)] utilizing the same quantum channel is made and shows its distinct advantage of degrading the intensity and difficulty of necessary operations.
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.
Abstract A four-party deterministic single-qubit operation sharing scheme is proposed by using a generalized seven-qubit Brown state in a given qubit distribution as the quantum channel. Its security is confirmed via analyses. The sharing determinacy and the sharer symmetry of the scheme are identified. The experimental feasibility of the scheme is confirmed through discussions. Moreover, the scheme is compared with a competing one which utilizes the same quantum channel. It is found that the present scheme reduces the necessary operations and two-qubit unitary operation types as well as the classical communication cost. The decreases of both the necessary operation complexity and the classical communication cost eventually mean both the increase of the scheme efficiency and the decrease of the resource consumption. Consequently, the present scheme is superior to the competing 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.
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 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.