Scheme for directly measuring the concurrences of Collins–Gisin and Werner classes polarization entangled mixed states

We present a two-copy-based protocol for directly measuring the concurrence of two-photon polarization entangled mixed states (Collins–Gisin class state and the more complicated bipartite mixed entangled state—Werner class state) without quantum state tomography. The quantum circuit designed for directly measuring concurrence can be realized in an optical system. Our protocol works without the sophisticated controlled-NOT gate, which makes it much simpler than the previous ones. Because all the operations used here are local, the scheme can be used for directly measuring remote mixed entanglement too.

[1]  D. Deutsch.  Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

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

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

[4]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[5]  Pérès.  Separability Criterion for Density Matrices. , 1996, Physical review letters.

[6]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[7]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[8]  W. Wootters,et al.  Entanglement of a Pair of Quantum Bits , 1997, quant-ph/9703041.

[9]  H. Weinfurter,et al.  Experimental quantum teleportation , 1997, Nature.

[10]  Michael D. Westmoreland,et al.  Sending classical information via noisy quantum channels , 1997 .

[11]  Andrew G. White,et al.  Nonmaximally Entangled States: Production, Characterization, and Utilization , 1999, quant-ph/9908081.

[12]  P. Knight,et al.  Proposal for teleportation of an atomic state via cavity decay , 1999, quant-ph/9908004.

[13]  David P. DiVincenzo,et al.  Quantum information and computation , 2000, Nature.

[14]  William K. Wootters,et al.  Entanglement of formation and concurrence , 2001, Quantum Inf. Comput..

[15]  Andrew G. White,et al.  Measurement of qubits , 2001, quant-ph/0103121.

[16]  P. Horodecki,et al.  Method for direct detection of quantum entanglement. , 2001, Physical review letters.

[17]  N. Gisin,et al.  A relevant two qubit Bell inequality inequivalent to the CHSH inequality , 2003, quant-ph/0306129.

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

[19]  T. Spiller,et al.  Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities , 2004, quant-ph/0408117.

[20]  Los Alamos National Laboratory,et al.  Synthesizing arbitrary two-photon polarization mixed states , 2005, quant-ph/0501115.

[21]  M. Kus,et al.  Concurrence of mixed multipartite quantum States. , 2004, Physical review letters.

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

[23]  T. Spiller,et al.  Efficient optical quantum information processing , 2005, quant-ph/0506116.

[24]  Raymond G. Beausoleil,et al.  Optical quantum information processing utilizing weak nonlinearities: a little goes a long way , 2005, SPIE Optics + Photonics.

[25]  S. Walborn,et al.  Experimental determination of entanglement with a single measurement , 2006, Nature.

[26]  S. Fei,et al.  Concurrence-Based Entanglement Measure for Werner States , 2006, quant-ph/0702017.

[27]  M. Steffen,et al.  Measurement of the Entanglement of Two Superconducting Qubits via State Tomography , 2006, Science.

[28]  J. C. Retamal,et al.  Direct measurement of concurrence for atomic two-qubit pure states , 2006, quant-ph/0611016.

[29]  A. Buchleitner,et al.  Observable entanglement measure for mixed quantum States. , 2006, Physical review letters.

[30]  S. Walborn,et al.  Experimental Determination of Entanglement by a Projective Measurement , 2007 .

[31]  O. Osenda,et al.  Scaling of the von Neumann entropy in a two-electron system near the ionization threshold , 2007 .

[32]  Sergio Albeverio,et al.  Entanglement of formation and concurrence for mixed states , 2008, Frontiers of Computer Science in China.

[33]  Wei Song,et al.  Novel schemes for directly measuring entanglement of general states. , 2008, Physical review letters.

[34]  S. Hossenfelder.  Bimetric theory with exchange symmetry , 2008, 0807.2838.

[35]  Yang Rong-Can,et al.  Simple Scheme for Directly Measuring Concurrence of Two-Qubit Pure States in One Step , 2009 .

[36]  M. Koashi,et al.  Quantum repeaters and computation by a single module: Remote nondestructive parity measurement , 2010, 1003.0181.

[37]  Qing Yang,et al.  Direct measurement of the concurrence of two-photon polarization-entangled states , 2013 .

[38]  Ming Yang,et al.  Direct measurement of the concurrence for two-photon polarization entangled pure states by parity-check measurements , 2013 .

[39]  Ming Yang,et al.  Directly measuring the concurrence of atomic two-qubit states through the detection of cavity decay , 2014 .

[40]  Lan Zhou,et al.  Detection of the nonlocal atomic entanglement assisted with single photons , 2014, 1401.2526.

[41]  K. Życzkowski,et al.  Method for universal detection of two-photon polarization entanglement , 2014, 1405.5560.

[42]  Lan Zhou,et al.  Concurrence Measurement for the Two-Qubit Optical and Atomic States , 2015, Entropy.

[43]  Karol Bartkiewicz,et al.  Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix , 2014, 1411.7977.

[44]  Jun Pan,et al.  Two-step measurement of the concurrence for hyperentangled state , 2014, Quantum Inf. Process..

[45]  Shou Zhang,et al.  Direct measurement of nonlocal entanglement of two-qubit spin quantum states , 2016, Scientific Reports.