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 Letters

Deterministic Three-Copy Entanglement Concentration of Photons through Direct Sum Extension and Auxiliary Degrees of Freedom

Jie Zhao, Wendong Li, Yongjian Gu

Published Jul 1, 2013• 1 citation
Publisher

Abstract

The schematic optical realization of deterministic multicopy (three-copy) entanglement concentration under local operations and classical communication (LOCC) is presented, which can resort to the linear optical elements, controlled-NOT gate that uses weak cross-Kerr nonlinearity effect and entangled qudits with different degrees of freedom. This concentration is based on Nielsen's theorem, which in principle quantifies the unit success probability. In addition, the required positive operator-valued measurement (POVM) is implemented through direct sum extension, because the least number of ancillary dimensions is demanded. The construction of POVM is systematically formulated, which results in the feasibility to generate the protocol to n-copy (n > 3) cases.

DOI
10.1088/0256-307x/30/7/070302

Related papers

Deterministic multicopy entanglement concentration

Jie Zhao, Wendong Li, Yongjian Gu

The determinisitc entanglement concentration (DEC) protocol under local operations and classical communication (LOCC) for three-copy partially entangled states in bipartite systems is presented. The explicit elements of the operators used are calculated due to the general construction of the generalized measurement operator and the corresponding permutation matrices. The measurement is implemented based on the direct sum extension under the motivation to extend the initial state space with minimum number of ancillary dimensions. Morever, the concentration protocol is generalized to the DEC for n-copy multi-partite GHZ-class states. It is also pointed out that the formation of the measurement operator and the algorithms used to calculate its elements can be utilized in more general cases achieving the feasible entanglement transformation that is clarified by Nielsen's theorem, such as the transformation between arbitrary bipartite states in multicopy and high-dimensional cases and so does multi-partite GHZ-class states.

Europhysics Letters (EPL)•Oct 1, 2013•7 citations

Optimal deterministic entanglement concentration of polarized photons through direct sum extension

Wendong Li, Wen-Zhao Zhang, Ma Lizhen +1 more

A scheme for optimal deterministic entanglement concentration is proposed, and its corresponding optical realization based on a cavity-assisted linear optical system is presented. In this scheme, the quantum circuit devised is simpler than that built in [Y. J. Gu, et al. (2006), Phys. Rev. A. 73, 022321], as it requires the minimum ancillary dimensions and the number of unitary operations. Moreover, we show that, by introducing a path-polarization entanglement state based on the direct sum extension method, three elementary controlled phase-flip gates between two photons are sufficient in the design of its optical realization scheme, making it easy to be implemented from the experimental point of view. Meanwhile, the scheme is verified effective to recover highly entangled pairs from mixed states.

Quantum Information and Computation•Jul 1, 2011•1 citation

Efficient three-step entanglement concentration for an arbitrary four-photon cluster state

Bin Si, Shi‐Lei Su, Li-Li Sun +3 more

We propose an entanglement concentration protocol to concentrate an arbitrary partially-entangled four-photon cluster state. As a pioneering three-step entanglement concentration scheme, our protocol only needs a single-photon resource to assist the concentration in each step, which makes this protocol more economical. With the help of the linear optical elements and weak cross-Kerr nonlinearity, one can obtain a maximally-entangled cluster state via local operations and classical communication. Moreover, the protocol can be iterated to obtain a higher success probability and is feasible under current experimental conditions.

Chinese Physics B•Mar 1, 2013•23 citations

Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity

Li-Li Sun, Hong‐Fu Wang, Shou Zhang +1 more

We present two schemes to concentrate unknown partially entangled three-photon W states with weak cross-Kerr nonlinearity. In both schemes, the three distant parities can obtain a maximally entangled W state via local operations and classical communication with a higher success probability that is double that in Xiong and Ye’s scheme [J. Opt. Soc. Am. B28, 2030 (2011)]. The entanglement concentration schemes need only one party’s local operations. Our schemes are relatively simple because fewer linear optics elements are used. In addition, our schemes do not need to use sophisticated single-photon detectors, which makes the scheme more feasible with present techniques.

Journal of the Optical Society of America B•Mar 16, 2012•33 citations

Protocol and quantum circuits for realizing deterministic entanglement concentration

Yongjian Gu, Wendong Li, Guang‐Can Guo

Entanglement concentration can be achieved in a deterministic fashion [Morikoshi, Phys. Rev. Lett. 84, 3189 (2000); Phys. Rev. A 64, 022316 (2001)]. We present a protocol for deterministic extraction of an Einstein-Podolsky-Rosen pair from two partially entangled pairs via local operations and classical communication. This protocol consists of a generalized measurement described by a positive operator-valued measure (POVM), one-way classical communication, and a corresponding unitary operation or a choice between the two pairs. Based on the theory of majorization, we explicitly construct the required POVM, which can be realized by performing a unitary operation in the extended space and a conventional Von Neuman orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the deterministic entanglement concentration. Our method for constructing quantum circuits differs from the usual method based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.

Physical Review A•Feb 13, 2006•37 citations

Single-photon-assisted entanglement concentration of a multiphoton system in a partially entangled W state with weak cross-Kerr nonlinearity

Fang‐Fang Du, Tao Li, Bao‐Cang Ren +2 more

We propose a nonlocal entanglement concentration protocol (ECP) for N-photon systems in a partially entangled W state, resorting to some ancillary single photons and the parity-check measurement based on cross-Kerr nonlinearity. One party in quantum communication first performs a parity-check measurement on her photon in an N-photon system and an ancillary photon, and then she picks up the even-parity instance for obtaining the standard W state. When she obtains an odd-parity instance, the system is in a less-entanglement state, and it is the resource in the next round of entanglement concentration. By iterating the entanglement concentration process several times, the present ECP has a total success probability approaching the limit in theory. The present ECP has the advantage of a high success probability. Moreover, the present ECP requires only the N-photon system itself and some ancillary single photons, not two copies of the systems, which decreases the difficulty of its implementation greatly in experiment. It may have good applications in quantum communication in the future.

arXiv:1208.0105•Journal of the Optical Society of America B•May 22, 2012•40 citations
The schematic optical realization of deterministic multicopy (three-copy) entanglement concentration under local operations and classical communication (LOCC) is presented, which can resort to the linear optical elements, controlled-NOT gate that uses weak cross-Kerr nonlinearity effect and entangled qudits with different degrees of freedom. This concentration is based on Nielsen's theorem, which in principle quantifies the unit success probability. In addition, the required positive operator-valued measurement (POVM) is implemented through direct sum extension, because the least number of ancillary dimensions is demanded. The construction of POVM is systematically formulated, which results in the feasibility to generate the protocol to n-copy (n > 3) cases.
The determinisitc entanglement concentration (DEC) protocol under local operations and classical communication (LOCC) for three-copy partially entangled states in bipartite systems is presented. The explicit elements of the operators used are calculated due to the general construction of the generalized measurement operator and the corresponding permutation matrices. The measurement is implemented based on the direct sum extension under the motivation to extend the initial state space with minimum number of ancillary dimensions. Morever, the concentration protocol is generalized to the DEC for n-copy multi-partite GHZ-class states. It is also pointed out that the formation of the measurement operator and the algorithms used to calculate its elements can be utilized in more general cases achieving the feasible entanglement transformation that is clarified by Nielsen's theorem, such as the transformation between arbitrary bipartite states in multicopy and high-dimensional cases and so does multi-partite GHZ-class states.
A scheme for optimal deterministic entanglement concentration is proposed, and its corresponding optical realization based on a cavity-assisted linear optical system is presented. In this scheme, the quantum circuit devised is simpler than that built in [Y. J. Gu, et al. (2006), Phys. Rev. A. 73, 022321], as it requires the minimum ancillary dimensions and the number of unitary operations. Moreover, we show that, by introducing a path-polarization entanglement state based on the direct sum extension method, three elementary controlled phase-flip gates between two photons are sufficient in the design of its optical realization scheme, making it easy to be implemented from the experimental point of view. Meanwhile, the scheme is verified effective to recover highly entangled pairs from mixed states.
We propose an entanglement concentration protocol to concentrate an arbitrary partially-entangled four-photon cluster state. As a pioneering three-step entanglement concentration scheme, our protocol only needs a single-photon resource to assist the concentration in each step, which makes this protocol more economical. With the help of the linear optical elements and weak cross-Kerr nonlinearity, one can obtain a maximally-entangled cluster state via local operations and classical communication. Moreover, the protocol can be iterated to obtain a higher success probability and is feasible under current experimental conditions.
We present two schemes to concentrate unknown partially entangled three-photon W states with weak cross-Kerr nonlinearity. In both schemes, the three distant parities can obtain a maximally entangled W state via local operations and classical communication with a higher success probability that is double that in Xiong and Ye’s scheme [J. Opt. Soc. Am. B28, 2030 (2011)]. The entanglement concentration schemes need only one party’s local operations. Our schemes are relatively simple because fewer linear optics elements are used. In addition, our schemes do not need to use sophisticated single-photon detectors, which makes the scheme more feasible with present techniques.
Entanglement concentration can be achieved in a deterministic fashion [Morikoshi, Phys. Rev. Lett. 84, 3189 (2000); Phys. Rev. A 64, 022316 (2001)]. We present a protocol for deterministic extraction of an Einstein-Podolsky-Rosen pair from two partially entangled pairs via local operations and classical communication. This protocol consists of a generalized measurement described by a positive operator-valued measure (POVM), one-way classical communication, and a corresponding unitary operation or a choice between the two pairs. Based on the theory of majorization, we explicitly construct the required POVM, which can be realized by performing a unitary operation in the extended space and a conventional Von Neuman orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the deterministic entanglement concentration. Our method for constructing quantum circuits differs from the usual method based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.
We propose a nonlocal entanglement concentration protocol (ECP) for N-photon systems in a partially entangled W state, resorting to some ancillary single photons and the parity-check measurement based on cross-Kerr nonlinearity. One party in quantum communication first performs a parity-check measurement on her photon in an N-photon system and an ancillary photon, and then she picks up the even-parity instance for obtaining the standard W state. When she obtains an odd-parity instance, the system is in a less-entanglement state, and it is the resource in the next round of entanglement concentration. By iterating the entanglement concentration process several times, the present ECP has a total success probability approaching the limit in theory. The present ECP has the advantage of a high success probability. Moreover, the present ECP requires only the N-photon system itself and some ancillary single photons, not two copies of the systems, which decreases the difficulty of its implementation greatly in experiment. It may have good applications in quantum communication in the future.