Computable and Operationally Meaningful Multipartite Entanglement Measures

Beckey, Jacob L.; Gigena, N.; Coles, Patrick J.; Cerezo de la Roca, Marco Vinicio Sebastian

doi:10.1103/physrevlett.127.140501

Computable and Operationally Meaningful Multipartite Entanglement Measures

Journal Article · Mon Sep 27 00:00:00 EDT 2021 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.127.140501· OSTI ID:1992261

^[1]; ^[2]; Coles, Patrick J. ^[3]; ^[3]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Univ. of Colorado, Boulder, CO (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Quantum Science Center (QSC)
Univ. of Warsaw (Poland)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Quantum Science Center (QSC)

Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state |ψ$$\rangle$$ for these applications is often directly related to the degree or type of entanglement present in |ψ$$\rangle$$. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. Here, in this work, we introduce a family of multipartite entanglement measures, called concentratable entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under local operations and classical communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1992261

Report Number(s):: LA-UR--22-23063

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 14 Vol. 127; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (51)

Quantum Information Theory Wilde, Mark M. https://doi.org/10.1017/CBO9781139525343	book	May 2013
The quantum internet Kimble, H. J. Nature, Vol. 453, Issue 7198 https://doi.org/10.1038/nature07127	journal	June 2008
Quantum teleportation over 143 kilometres using active feed-forward Ma, Xiao-Song; Herbst, Thomas; Scheidl, Thomas Nature, Vol. 489, Issue 7415 https://doi.org/10.1038/nature11472	journal	September 2012
Satellite-to-ground quantum key distribution Liao, Sheng-Kai; Cai, Wen-Qi; Liu, Wei-Yue Nature, Vol. 549, Issue 7670 https://doi.org/10.1038/nature23655	journal	August 2017
Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom Chalopin, Thomas; Bouazza, Chayma; Evrard, Alexandre Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-07433-1	journal	November 2018
Entanglement-enhanced sensor networks Pezzè, Luca Nature Photonics, Vol. 15, Issue 2 https://doi.org/10.1038/s41566-020-00755-x	journal	January 2021
Distributed quantum sensing in a continuous-variable entangled network Guo, Xueshi; Breum, Casper R.; Borregaard, Johannes Nature Physics https://doi.org/10.1038/s41567-019-0743-x	journal	December 2019
Quantum supremacy using a programmable superconducting processor Arute, Frank; Arya, Kunal; Babbush, Ryan Nature, Vol. 574, Issue 7779 https://doi.org/10.1038/s41586-019-1666-5	journal	October 2019
Global entanglement in multiparticle systems Meyer, David A.; Wallach, Nolan R. Journal of Mathematical Physics, Vol. 43, Issue 9 https://doi.org/10.1063/1.1497700	journal	September 2002
Teleportation, entanglement and thermodynamics in the quantum world Plenio, Martin B.; Vedral, Vlatko Contemporary Physics, Vol. 39, Issue 6 https://doi.org/10.1080/001075198181766	journal	November 1998
Monotones and invariants for multi-particle quantum states Barnum, H.; Linden, N. Journal of Physics A: Mathematical and General, Vol. 34, Issue 35 https://doi.org/10.1088/0305-4470/34/35/305	journal	August 2001
Learning the quantum algorithm for state overlap Cincio, Lukasz; Subaşı, Yiğit; Sornborger, Andrew T. New Journal of Physics, Vol. 20, Issue 11 https://doi.org/10.1088/1367-2630/aae94a	journal	November 2018
Entanglement spectroscopy with a depth-two quantum circuit Subaşı, Yiğit; Cincio, Lukasz; Coles, Patrick J. Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 4 https://doi.org/10.1088/1751-8121/aaf54d	journal	January 2019
The controlled SWAP test for determining quantum entanglement Foulds, Steph; Kendon, Viv; Spiller, Tim Quantum Science and Technology, Vol. 6, Issue 3 https://doi.org/10.1088/2058-9565/abe458	journal	April 2021
Quantum algorithms: entanglement–enhanced information processing Ekert, Artur; Jozsa, Richard Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 356, Issue 1743 https://doi.org/10.1098/rsta.1998.0248	journal	August 1998
Teleportation Systems Toward a Quantum Internet Valivarthi, Raju; Davis, Samantha I.; Peña, Cristián PRX Quantum, Vol. 1, Issue 2 https://doi.org/10.1103/PRXQuantum.1.020317	journal	December 2020
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Einstein, A.; Podolsky, B.; Rosen, N. Physical Review, Vol. 47, Issue 10 https://doi.org/10.1103/PhysRev.47.777	journal	May 1935
Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states Coles, Patrick J.; Cerezo, M.; Cincio, Lukasz Physical Review A, Vol. 100, Issue 2 https://doi.org/10.1103/PhysRevA.100.022103	journal	August 2019
One-body entanglement as a quantum resource in fermionic systems Gigena, N.; Di Tullio, M.; Rossignoli, R. Physical Review A, Vol. 102, Issue 4 https://doi.org/10.1103/PhysRevA.102.042410	journal	October 2020
Substituting quantum entanglement for communication Cleve, Richard; Buhrman, Harry Physical Review A, Vol. 56, Issue 2 https://doi.org/10.1103/PhysRevA.56.1201	journal	August 1997
Distributed entanglement Coffman, Valerie; Kundu, Joydip; Wootters, William K. Physical Review A, Vol. 61, Issue 5 https://doi.org/10.1103/PhysRevA.61.052306	journal	April 2000
Three qubits can be entangled in two inequivalent ways Dür, W.; Vidal, G.; Cirac, J. I. Physical Review A, Vol. 62, Issue 6 https://doi.org/10.1103/PhysRevA.62.062314	journal	November 2000
Potential multiparticle entanglement measure Wong, Alexander; Christensen, Nelson Physical Review A, Vol. 63, Issue 4 https://doi.org/10.1103/PhysRevA.63.044301	journal	March 2001
Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality Barrett, Jonathan Physical Review A, Vol. 65, Issue 4 https://doi.org/10.1103/PhysRevA.65.042302	journal	March 2002
Classification of multipartite entangled states by multidimensional determinants Miyake, Akimasa Physical Review A, Vol. 67, Issue 1 https://doi.org/10.1103/PhysRevA.67.012108	journal	January 2003
Entanglement, mixedness, and spin-flip symmetry in multiple-qubit systems Jaeger, Gregg; Sergienko, Alexander V.; Saleh, Bahaa E. A. Physical Review A, Vol. 68, Issue 2 https://doi.org/10.1103/PhysRevA.68.022318	journal	August 2003
Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions Scott, A. J. Physical Review A, Vol. 69, Issue 5 https://doi.org/10.1103/PhysRevA.69.052330	journal	May 2004
Entanglement and the power of one qubit Datta, Animesh; Flammia, Steven T.; Caves, Carlton M. Physical Review A, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevA.72.042316	journal	October 2005
Critical sets of the total variance can detect all stochastic local operations and classical communication classes of multiparticle entanglement Sawicki, Adam; Oszmaniec, Michał; Kuś, Marek Physical Review A, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevA.86.040304	journal	October 2012
Bipartite entanglement in fermion systems Gigena, N.; Rossignoli, R. Physical Review A, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevA.95.062320	journal	June 2017
Longer-Baseline Telescopes Using Quantum Repeaters Gottesman, Daniel; Jennewein, Thomas; Croke, Sarah Physical Review Letters, Vol. 109, Issue 7 https://doi.org/10.1103/PhysRevLett.109.070503	journal	August 2012
Truncated Nonlinear Interferometry for Quantum-Enhanced Atomic Force Microscopy Pooser, R. C.; Savino, N.; Batson, E. Physical Review Letters, Vol. 124, Issue 23 https://doi.org/10.1103/PhysRevLett.124.230504	journal	June 2020
Genuine Network Multipartite Entanglement Navascués, Miguel; Wolfe, Elie; Rosset, Denis Physical Review Letters, Vol. 125, Issue 24 https://doi.org/10.1103/PhysRevLett.125.240505	journal	December 2020
Quantum optical Fredkin gate Milburn, G. J. Physical Review Letters, Vol. 62, Issue 18 https://doi.org/10.1103/PhysRevLett.62.2124	journal	May 1989
Quantum cryptography based on Bell’s theorem Ekert, Artur K. Physical Review Letters, Vol. 67, Issue 6 https://doi.org/10.1103/PhysRevLett.67.661	journal	August 1991
Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels Bennett, Charles H.; Brassard, Gilles; Crépeau, Claude Physical Review Letters, Vol. 70, Issue 13 https://doi.org/10.1103/PhysRevLett.70.1895	journal	March 1993
Entanglement of Formation of an Arbitrary State of Two Qubits Wootters, William K. Physical Review Letters, Vol. 80, Issue 10 https://doi.org/10.1103/PhysRevLett.80.2245	journal	March 1998
Conditions for a Class of Entanglement Transformations Nielsen, M. A. Physical Review Letters, Vol. 83, Issue 2 https://doi.org/10.1103/PhysRevLett.83.436	journal	July 1999
Generalized Schmidt Decomposition and Classification of Three-Quantum-Bit States Acín, A.; Andrianov, A.; Costa, L. Physical Review Letters, Vol. 85, Issue 7 https://doi.org/10.1103/PhysRevLett.85.1560	journal	August 2000
Quantum Fingerprinting Buhrman, Harry; Cleve, Richard; Watrous, John Physical Review Letters, Vol. 87, Issue 16 https://doi.org/10.1103/PhysRevLett.87.167902	journal	September 2001
Multipartite Entanglement Detection in Bosons Moura Alves, C.; Jaksch, D. Physical Review Letters, Vol. 93, Issue 11 https://doi.org/10.1103/PhysRevLett.93.110501	journal	September 2004
Decoherence and Multipartite Entanglement Carvalho, André R. R.; Mintert, Florian; Buchleitner, Andreas Physical Review Letters, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevLett.93.230501	journal	December 2004
Detecting Genuine Multipartite Entanglement with Two Local Measurements Tóth, Géza; Gühne, Otfried Physical Review Letters, Vol. 94, Issue 6 https://doi.org/10.1103/PhysRevLett.94.060501	journal	February 2005
Quantum cryptography Gisin, Nicolas; Ribordy, Grégoire; Tittel, Wolfgang Reviews of Modern Physics, Vol. 74, Issue 1 https://doi.org/10.1103/RevModPhys.74.145	journal	March 2002
Quantum entanglement Horodecki, Ryszard; Horodecki, Paweł; Horodecki, Michał Reviews of Modern Physics, Vol. 81, Issue 2 https://doi.org/10.1103/RevModPhys.81.865	journal	June 2009
Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information Walter, M.; Doran, B.; Gross, D. Science, Vol. 340, Issue 6137 https://doi.org/10.1126/science.1232957	journal	June 2013
Quantum internet: A vision for the road ahead Wehner, Stephanie; Elkouss, David; Hanson, Ronald Science, Vol. 362, Issue 6412 https://doi.org/10.1126/science.aam9288	journal	October 2018
Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization Harrow, Aram W.; Montanaro, Ashley Journal of the ACM, Vol. 60, Issue 1 https://doi.org/10.1145/2432622.2432625	journal	February 2013
Majorization and the interconversion of bipartite states Nielsen, Michael; Vidal, Guifre Quantum Information and Computation, Vol. 1, Issue 1 https://doi.org/10.26421/QIC1.1-5	journal	July 2001
Quantum Interactive Proofs and the Complexity of Separability Testing Gutoski, Gus; Hayden, Patrick; Milner, Kevin Theory of Computing, Vol. 11, Issue 1, p. 59-103 https://doi.org/10.4086/toc.2015.v011a003	journal	March 2015
Quantum supremacy using a programmable superconducting processor Martinis, John; Boixo, Sergio; Neven, Hartmut Dryad https://doi.org/10.5061/dryad.k6t1rj8	dataset	January 2019

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Computable and Operationally Meaningful Multipartite Entanglement Measures

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