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

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.

[1]  M. Koashi,et al.  Quantum entanglement for secret sharing and secret splitting , 1999 .

[2]  G. Long,et al.  Theoretically efficient high-capacity quantum-key-distribution scheme , 2000, quant-ph/0012056.

[3]  Quantum information splitting of an arbitrary three-qubit state via the cavity input–output process , 2012 .

[4]  R. G. Beausoleil,et al.  High-efficiency quantum-nondemolition single-photon-number-resolving detector , 2005 .

[5]  李熙涵,et al.  Faithful quantum entanglement sharing based on linear optics with additional qubits , 2009 .

[6]  Jian-Wei Pan,et al.  Practical scheme for entanglement concentration , 2001, quant-ph/0104039.

[7]  Ming Yang,et al.  Entanglement concentration for unknown W class states , 2007 .

[8]  Shou Zhang,et al.  Generating a four-photon polarization-entangled cluster state with homodyne measurement via cross-Kerr nonlinearity , 2012 .

[9]  W. Munro,et al.  A near deterministic linear optical CNOT gate , 2004 .

[10]  Keiji Sasaki,et al.  Demonstration of an optical quantum controlled-NOT gate without path interference. , 2005, Physical review letters.

[11]  W. Bowen,et al.  Tripartite quantum state sharing. , 2003, Physical review letters.

[12]  M. J. Fitch,et al.  Experimental controlled-NOT logic gate for single photons in the coincidence basis , 2003, quant-ph/0303095.

[13]  Shou Zhang,et al.  Entanglement concentration of partially entangled three-photon W states with weak cross-Kerr nonlinearity , 2012 .

[14]  Jian-Wei Pan,et al.  Optical Nondestructive Controlled-NOT Gate without Using Entangled Photons , 2007 .

[15]  Qi Guo,et al.  Simplified optical quantum-information processing via weak cross-Kerr nonlinearities , 2011 .

[16]  Géza Tóth,et al.  Experimental analysis of a four-qubit photon cluster state. , 2005, Physical review letters.

[17]  Bing He,et al.  Single-photon logic gates using minimal resources , 2009, 0909.0300.

[18]  Philip Walther,et al.  Experimental violation of a cluster state bell inequality. , 2005, Physical review letters.

[19]  Shengmei Zhao,et al.  Efficient two-step entanglement concentration for arbitrary W states , 2012, 1202.3019.

[20]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

[21]  Cao Zhuo-liang,et al.  Scheme for entanglement concentration of unknown W class states via linear optics , 2007 .

[22]  B. Zheng,et al.  Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs , 2012, 1202.2190.

[23]  Jaromir Fiurasek.  Linear-optics quantum Toffoli and Fredkin gates , 2006 .

[24]  M. Koashi,et al.  Concentration and purification scheme for two partially entangled photon pairs , 2001, quant-ph/0101042.

[25]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[26]  Fuguo Deng,et al.  Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics , 2008, 0806.0115.

[27]  Shou Zhang,et al.  Linear optical scheme for entanglement concentration of two partially entangled three-photon ${\sf W}$ states , 2010 .

[28]  Xin-Wen Wang,et al.  Dense coding and teleportation with one-dimensional cluster states , 2007 .

[29]  Ting Gao,et al.  Two local observables are sufficient to characterize maximally entangled states of N qubits , 2010, 1011.0987.

[30]  J. Cirac,et al.  Three qubits can be entangled in two inequivalent ways , 2000, quant-ph/0005115.

[31]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[32]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[33]  Kae Nemoto,et al.  Weak nonlinearities: a new route to optical quantum computation , 2005, quant-ph/0507084.

[34]  Jian Li,et al.  Quantum control gates with weak cross-Kerr nonlinearity , 2008, 0811.3364.

[35]  An-Ning Zhang,et al.  Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits. , 2004, Physical review letters.

[36]  S. Bose,et al.  PURIFICATION VIA ENTANGLEMENT SWAPPING AND CONSERVED ENTANGLEMENT , 1998, quant-ph/9812013.

[37]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[38]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[39]  Gu Bin,et al.  A two-step quantum secure direct communication protocol with hyperentanglement , 2011 .

[40]  Wolfgang Mathis,et al.  Generating a four-photon polarization-entangled cluster state , 2005 .

[41]  Zhang Wen,et al.  Teleportation of arbitrary unknown two-atom state with cluster state via thermal cavity , 2008 .

[42]  W Dür,et al.  Stability of macroscopic entanglement under decoherence. , 2004, Physical review letters.