Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics

Probabilistically implementing nonlocal operations between two distant qutrits

Shan Yong-Guang, Jianjun Nie, Zeng Hao-Sheng

Published May 31, 2006• 2 citations
Publisher

Abstract

We propose a method to probabilistically implement a nonlocal operation, exp[iξ U A U B ], between two distant qutrits A and B , where ξ∊[0,2π] and U A , U B are local unitary and Hermitian operations for qutrits A and B respectively. The consumptions of resource for one performance of the method are a single non-maximally entangled qutrit state and 1-trit classical communication. For a given ξ, the successful probability of the method depends on the forms of both entanglement resource and Bob's partial-measurement basis. We systematically discuss the optimal successful probabilities and their corresponding conditions for three cases: adjustable entanglement resource, adjustable partial-measurement basis, adjustable entanglement resource and partial-measurement basis. It is straightforward to generalize the method for producing nonlocal unitary operations between any two N -level systems.

DOI
10.1088/1009-1963/15/6/009

Related papers

Probabilistic Implementation of Non-Local CNOT Operation and Entanglement Purification

Yi-Zhuang Zheng, Peng Ye, Guo Guang-Can

We propose a protocol for implementation of nonlocal CNOT operation using a partially entangled channel and show that when partially entangled pairs are taken as quantum channels, the nonlocal CNOT operation can be implemented probabilistically by introducing a collective unitary transformation. The required resources for implementation of the nonlocal CNOT operation in this case are discussed. We also point out that the nonlocal CNOT operation can be used as a purification protocol to concentrate entanglement from an ensemble of partially entangled particles into a subensemble of maximally entanglement ones.

Chinese Physics Letters•Jan 1, 2004•21 citations

Probabilistic Implementation of Non-Local CNOT Operation and Entanglement Purification

郑亦庄, 叶鹏, 郭光灿

We propose a protocol for implementation of nonlocal CNOT operation using a partially entangled channel and show that when partially entangled pairs are taken as quantum channels, the nonlocal CNOT operation can be implemented probabilistically by introducing a collective unitary transformation. The required resources for implementation of the nonlocal CNOT operation in this case are discussed. We also point out that the nonlocal CNOT operation can be used as a puritlcation protocol to concentrate entanglement from an ensemble of partially entangled particles into a subensemble of maximally entanglement ones.

Chinese Physics Letters•Jan 1, 2004•0 citations

Probabilistic implementation of a nonlocal operation using a nonmaximally entangled state

Lin Chen, Yi-Xin Chen

We develop the probabilistic implementation of a nonlocal gate $\mathrm{exp}[i\ensuremath{\xi}{\ensuremath{\sigma}}_{{n}_{A}}{\ensuremath{\sigma}}_{{n}_{B}}]$ and $\ensuremath{\xi}∊[0,(\ensuremath{\pi}∕4)]$, by using a single nonmaximally entangled state. We prove that nonlocal gates can be implemented with a fidelity of $>79.3%$ and a consumption of $<0.969\phantom{\rule{0.3em}{0ex}}\mathrm{ebits}$ and two classical bits, when $\ensuremath{\xi}\ensuremath{\leqslant}0.353$. This provides a higher bound for the feasible operation compared to the former techniques. Besides, gates with $\ensuremath{\xi}\ensuremath{\geqslant}0.353$ can be implemented with the probability 79.3% and a consumption of 0.969 ebits, which is the same efficiency as the distillation-based protocol, while our method saves extra classical resources. Gates with $\ensuremath{\xi}\ensuremath{\rightarrow}0$ can be implemented with nearly unit probability and a small entanglement. We also generalize some applications to the multiple system, where we find it is possible to implement certain nonlocal gates between many nonentangled partners using a nonmaximally multiple entangled state.

arXiv:quant-ph/0501107•Physical Review A•May 17, 2005•27 citations

REMOTE INTERACTIONS ON DISTRIBUTED QUANTUM SYSTEMS: NON-LOCAL CONDITIONAL OPERATIONS AND PRODUCTION OF MULTIPARTICLE ENTANGLED STATE

Libing Chen, Haiping Lu, Weicheng Chen

We present a systematic simple method for constructing non-local quantum conditional rotation with single target and multiple targets operations. We firstly show how a non-local conditional rotation with single target operation can be implemented with unit fidelity and unit probability by using a maximally entangled pair as quantum channel. We also put forward a scheme for probabilistically implementing the operation with unit fidelity by employing a partially entangled pair as quantum channel. The required physical resources for implementation of the non-local operation in these two cases are discussed. We further consider non-local conditional rotation with multiple targets operations on N spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initially distributed between systems. We also point out that the non-local conditional rotation operation can be used to generate multiparticle entanglement between particles belonging to distant users in a communication network and distributed quantum computer.

International Journal of Modern Physics B•Aug 10, 2005•2 citations

Implementation of nonlocal quantum swap operation on two entangled pairs

Yi-Zhuang Zheng, Gu Yong-Jian, Libing Chen +1 more

We propose a scheme for the implementation of nonlocal quantum swap operation on two spatially separated entangled pairs and we show that the operation can swap two qubits of these entangled pairs. We discuss the resources of the entangled qubits and classical communication bits required for the optimal implementation of the nonlocal quantum swap operation. We also put forward a scheme for probabilistic implementation of nonlocal swap operation via a nonmaximally entangled quantum channel. The probability of a successful nonlocal swap operation is obtained by introducing a collective unitary transformation.

Chinese Physics•May 14, 2002•16 citations

Generalized three-party sharing of operations on remote single qutrit

Pengfei Xing, Yimin Liu, Chuanmei Xie +2 more

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.

International Journal of Quantum Information•Apr 1, 2014•2 citations
We propose a method to probabilistically implement a nonlocal operation, exp[iξ U A U B ], between two distant qutrits A and B , where ξ∊[0,2π] and U A , U B are local unitary and Hermitian operations for qutrits A and B respectively. The consumptions of resource for one performance of the method are a single non-maximally entangled qutrit state and 1-trit classical communication. For a given ξ, the successful probability of the method depends on the forms of both entanglement resource and Bob's partial-measurement basis. We systematically discuss the optimal successful probabilities and their corresponding conditions for three cases: adjustable entanglement resource, adjustable partial-measurement basis, adjustable entanglement resource and partial-measurement basis. It is straightforward to generalize the method for producing nonlocal unitary operations between any two N -level systems.
We propose a protocol for implementation of nonlocal CNOT operation using a partially entangled channel and show that when partially entangled pairs are taken as quantum channels, the nonlocal CNOT operation can be implemented probabilistically by introducing a collective unitary transformation. The required resources for implementation of the nonlocal CNOT operation in this case are discussed. We also point out that the nonlocal CNOT operation can be used as a purification protocol to concentrate entanglement from an ensemble of partially entangled particles into a subensemble of maximally entanglement ones.
We propose a protocol for implementation of nonlocal CNOT operation using a partially entangled channel and show that when partially entangled pairs are taken as quantum channels, the nonlocal CNOT operation can be implemented probabilistically by introducing a collective unitary transformation. The required resources for implementation of the nonlocal CNOT operation in this case are discussed. We also point out that the nonlocal CNOT operation can be used as a puritlcation protocol to concentrate entanglement from an ensemble of partially entangled particles into a subensemble of maximally entanglement ones.
We develop the probabilistic implementation of a nonlocal gate $\mathrm{exp}[i\ensuremath{\xi}{\ensuremath{\sigma}}_{{n}_{A}}{\ensuremath{\sigma}}_{{n}_{B}}]$ and $\ensuremath{\xi}∊[0,(\ensuremath{\pi}∕4)]$, by using a single nonmaximally entangled state. We prove that nonlocal gates can be implemented with a fidelity of >79.3>79.3%>79.3 and a consumption of <0.969ebits<0.969\phantom{\rule{0.3em}{0ex}}\mathrm{ebits}<0.969ebits and two classical bits, when $\ensuremath{\xi}\ensuremath{\leqslant}0.353$. This provides a higher bound for the feasible operation compared to the former techniques. Besides, gates with $\ensuremath{\xi}\ensuremath{\geqslant}0.353$ can be implemented with the probability 79.3% and a consumption of 0.969 ebits, which is the same efficiency as the distillation-based protocol, while our method saves extra classical resources. Gates with $\ensuremath{\xi}\ensuremath{\rightarrow}0$ can be implemented with nearly unit probability and a small entanglement. We also generalize some applications to the multiple system, where we find it is possible to implement certain nonlocal gates between many nonentangled partners using a nonmaximally multiple entangled state.
We present a systematic simple method for constructing non-local quantum conditional rotation with single target and multiple targets operations. We firstly show how a non-local conditional rotation with single target operation can be implemented with unit fidelity and unit probability by using a maximally entangled pair as quantum channel. We also put forward a scheme for probabilistically implementing the operation with unit fidelity by employing a partially entangled pair as quantum channel. The required physical resources for implementation of the non-local operation in these two cases are discussed. We further consider non-local conditional rotation with multiple targets operations on N spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initially distributed between systems. We also point out that the non-local conditional rotation operation can be used to generate multiparticle entanglement between particles belonging to distant users in a communication network and distributed quantum computer.
We propose a scheme for the implementation of nonlocal quantum swap operation on two spatially separated entangled pairs and we show that the operation can swap two qubits of these entangled pairs. We discuss the resources of the entangled qubits and classical communication bits required for the optimal implementation of the nonlocal quantum swap operation. We also put forward a scheme for probabilistic implementation of nonlocal swap operation via a nonmaximally entangled quantum channel. The probability of a successful nonlocal swap operation is obtained by introducing a collective unitary transformation.
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.