Quantum networks for concentrating entanglement

If two parties, Alice and Bob, share some number, n, of partially entangled pairs of qubits, then it is possible for them to concentrate these pairs into some smaller number of maximally entangled states. We present a simplified version of the algorithm for such entanglement concentration, and we describe efficient networks for implementing these operations.

[1]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[2]  R. Feynman.  Simulating physics with computers , 1999 .

[3]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

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

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

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

[7]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

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

[9]  Gilles Brassard,et al.  Tight bounds on quantum searching , 1996, quant-ph/9605034.

[10]  Gilles Brassard,et al.  An exact quantum polynomial-time algorithm for Simon's problem , 1997, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems.

[11]  Avi Wigderson,et al.  Quantum vs. classical communication and computation , 1998, STOC '98.

[12]  Gilles Brassard,et al.  Quantum Counting , 1998, ICALP.

[13]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  Ran Raz,et al.  Exponential separation of quantum and classical communication complexity , 1999, STOC '99.

[15]  G. Brassard,et al.  Quantum Amplitude Amplification and Estimation , 2000, quant-ph/0005055.

[16]  Michele Mosca,et al.  Quantum Computer Algorithms , 2003 .