Global versus local quantum correlations in the Grover search algorithm

Quantum correlations are thought to be the reason why certain quantum algorithms overcome their classical counterparts. Since the nature of this resource is still not fully understood, we shall investigate how entanglement and nonlocality among register qubits vary as the Grover search algorithm is run. We shall encounter pronounced differences between the measures employed as far as bipartite and global correlations are concerned.

[1]  J. Latorre,et al.  Universality of entanglement and quantum-computation complexity , 2003, quant-ph/0311017.

[2]  M. Casas,et al.  Nonlocality and entanglement in the XY model , 2010, 1007.0983.

[3]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[4]  J. Batle,et al.  Nonlocality and entanglement in qubit systems , 2011, 1102.4653.

[5]  B. Tsirelson Quantum analogues of the Bell inequalities. The case of two spatially separated domains , 1987 .

[6]  Hoi-Kwong Lo,et al.  Introduction to Quantum Computation Information , 2002 .

[7]  Yaakov S. Weinstein,et al.  Matrix-element distributions as a signature of entanglement generation , 2005 .

[8]  A. Shimizu,et al.  Macroscopic entanglement in Quantum Computation , 2005, quant-ph/0505057.

[9]  Heng Fan,et al.  Correlations in the Grover search , 2009, 0904.2703.

[10]  Ardehali Bell inequalities with a magnitude of violation that grows exponentially with the number of particles. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[11]  W Dür,et al.  Spin gases: quantum entanglement driven by classical kinematics. , 2005, Physical review letters.

[12]  Svetlichny,et al.  Distinguishing three-body from two-body nonseparability by a Bell-type inequality. , 1987, Physical review. D, Particles and fields.

[13]  Colin P. Williams,et al.  Explorations in quantum computing , 1997 .

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

[15]  R. Jozsa,et al.  Quantum Computation and Shor's Factoring Algorithm , 1996 .

[16]  R. Cleve,et al.  HOW TO SHARE A QUANTUM SECRET , 1999, quant-ph/9901025.

[17]  William J. Munro,et al.  Entanglement and its role in Shor's algorithm , 2006, Quantum Inf. Comput..

[18]  H. Briegel,et al.  Persistent entanglement in arrays of interacting particles. , 2000, Physical review letters.

[19]  A. V. Belinskii,et al.  Interference of light and Bell's theorem , 1993 .

[20]  V. Scarani,et al.  Bell-type inequalities to detect true n-body nonseparability. , 2002, Physical review letters.

[21]  Kiel T. Williams,et al.  Extreme quantum entanglement in a superposition of macroscopically distinct states. , 1990, Physical review letters.

[22]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[23]  V. Scarani,et al.  Nonlocality of cluster states of qubits , 2004, quant-ph/0405119.

[24]  D. Gottesman Theory of fault-tolerant quantum computation , 1997, quant-ph/9702029.

[25]  B. Tsirelson Some results and problems on quan-tum Bell-type inequalities , 1993 .

[26]  Florian Mintert,et al.  Measuring multipartite concurrence with a single factorizable observable. , 2006, Physical review letters.

[27]  M. Seevinck,et al.  Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations. , 2002, Physical review letters.

[28]  D. Meyer,et al.  Global entanglement in multiparticle systems , 2001, quant-ph/0108104.

[29]  Zhiwei Zhou,et al.  Multipartite entanglement in Grover’s search algorithm , 2012, Natural Computing.

[30]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[31]  Colin P. Williams Quantum Computing and Quantum Communications , 1999, Lecture Notes in Computer Science.

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

[33]  W. Wootters,et al.  Distributed Entanglement , 1999, quant-ph/9907047.

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

[35]  Andreas Buchleitner,et al.  Decoherence and multipartite entanglement. , 2004, Physical review letters.

[36]  C. Macchiavello,et al.  Scale invariance of entanglement dynamics in Grover's quantum search algorithm , 2013 .

[37]  V. Subrahmanyam,et al.  Multipartite entanglement in a one-dimensional time-dependent Ising model , 2004 .

[38]  A. J. Scott Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions , 2003, quant-ph/0310137.

[39]  Gavin K. Brennen An observable measure of entanglement for pure states of multi-qubit systems , 2003, Quantum Inf. Comput..

[40]  G. Doolen,et al.  Introduction to Quantum Computers , 1998 .

[41]  Dagomir Kaszlikowski,et al.  Entanglement in the Grover search algorithm , 2005 .

[42]  G. Vidal Efficient classical simulation of slightly entangled quantum computations. , 2003, Physical review letters.

[43]  S. Stepney,et al.  Searching for highly entangled multi-qubit states , 2005 .

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

[45]  B. Toner Monogamy of non-local quantum correlations , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[46]  Subhashish Banerjee,et al.  Entanglement in the Grover's Search Algorithm , 2013, ArXiv.

[47]  A. Galindo,et al.  Information and computation: Classical and quantum aspects , 2001, quant-ph/0112105.

[48]  H. Bechmann-Pasquinucci,et al.  Bell inequality, Bell states and maximally entangled states for n qubits , 1998, quant-ph/9804045.

[49]  M. Cao,et al.  Thermal entanglement between alternate qubits of a four-qubit heisenberg XX chain in a magnetic field , 2005 .

[50]  Yaakov S Weinstein,et al.  Entanglement generation of nearly random operators. , 2005, Physical review letters.

[51]  O. Biham,et al.  Entangled quantum states generated by Shor's factoring algorithm (6 pages) , 2005, quant-ph/0510042.