SPECIAL ISSUE: The Korepin Festschrift From Statistical Mechanics to Quantum Information Science A Collection of Articles Written in Honor of the 60th Birthday of Vladimir KorepinNo Access

MONOGAMY OF ENTANGLEMENT, N-REPRESENTABILITY PROBLEMS AND GROUND STATES

TZU-CHIEH WEI

TZU-CHIEH WEI

C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, NY 11794-3840, USA

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https://doi.org/10.1142/S021797921243014XCited by:0 (Source: Crossref)

Abstract

Monogamy of entanglement is a quantum mechanical property that limits quantum correlations shared among many parties. In an example strongly interacting spin system we examine approaches for approximating the ground state energy both from above and below by mean-field and N-representability methods, respectively. Due to strong competition among the terms in the Hamiltonian, the resulting ground-state wavefunction, although is entangled, does not possess entanglement that is proportional to the system size, thus obeying the monogamy of entanglement.

Keywords:

PACS: 03.65.Ud, 03.67.Mn, 75.10.Dg

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References

V. E. Korepin , N. M. Bogoliubov and A. G. Izergin , Quantum Inverse Scattering Method and Correlation Functions ( Cambridge University Press , Cambridge , 1993 ) . Crossref, Google Scholar
M. Nielsen and I. Chuang , Quantum Computation and Quantum Information ( Cambridge University Press , Cambridge , 2000 ) . Google Scholar
A. Yu. Kitaev , A. H. Shen and M. N. Vyalyi , Classical and Quantum Computation ( AMS , Providence , 2002 ) . Crossref, Google Scholar
F. Barahona, J. Phys. A: Math. Gen. 15, 3241 (1982), DOI: 10.1088/0305-4470/15/10/028. Crossref, ADS, Google Scholar
S. Bravyi, e-print , arXiv:quant-ph/0602108 . Google Scholar
C. R. Laumannet al., Quantum Inf. Comput. 10, 1 (2010). Web of Science, Google Scholar
F. Verstraete and J. I. Cirac, Phys. Rev. B 73, 094423 (2006), DOI: 10.1103/PhysRevB.73.094423. Crossref, Web of Science, Google Scholar
V. Coffman, J. Kundu and W. K. Wootters, Phys. Rev. A 61, 052306 (2000), DOI: 10.1103/PhysRevA.61.052306. Crossref, Web of Science, Google Scholar
T. J. Osborne and F. Verstraete, Phys. Rev. Lett. 96, 220503 (2006), DOI: 10.1103/PhysRevLett.96.220503. Crossref, Web of Science, Google Scholar
A. J. Coleman, Rev. Mod. Phys. 35, 668 (1963), DOI: 10.1103/RevModPhys.35.668. Crossref, Web of Science, ADS, Google Scholar
C. A. Coulson, Rev. Mod. Phys. 32, 175 (1960), DOI: 10.1103/RevModPhys.32.170. Google Scholar
R. H. Trethold, Phys. Rev. 105, 1421 (1957). Web of Science, Google Scholar
A. J. Coleman and V. I. Yukalov , Reduced Density Matrices: Coulson's Challenge ( Springer , Berlin , 2000 ) . Crossref, Google Scholar
J. Cioslowski , Many-Electron Densities and Reduced Density Matrices ( Springer , Berlin , 2000 ) . Crossref, Google Scholar
Y.-K. Liu, The complexity of the consistency and N -representability problems for quantum states, Ph.D. Thesis, Unversity of California–San Diego (2007); also in e-print , arXiv:0712.3041 . Google Scholar
Y.-K. Liu, M. Christandl and F. Verstraete, Phys. Rev. Lett. 98, 110503 (2007), DOI: 10.1103/PhysRevLett.98.110503. Crossref, Web of Science, Google Scholar
T.-C. Wei, M. Mosca and A. Nayak, Phys. Rev. Lett. 104, 040501 (2010), DOI: 10.1103/PhysRevLett.104.040501. Crossref, Web of Science, Google Scholar
T.-C. Wei and P. M. Goldbart, Phys. Rev. A 68, 042307 (2003), DOI: 10.1103/PhysRevA.68.042307. Crossref, Web of Science, Google Scholar
T.-C. Wei, Phys. Rev. A 78, 012327 (2008), DOI: 10.1103/PhysRevA.78.012327. Crossref, Web of Science, Google Scholar
R. Hübeneret al., Phys. Rev. A 80, 032324 (2009). Crossref, Web of Science, Google Scholar
M. Hayashiet al., J. Math. Phys. 50, 122104 (2009), DOI: 10.1063/1.3271041. Crossref, Web of Science, ADS, Google Scholar
T.-C. Wei and S. Severini, J. Math. Phys. 51, 092203 (2010), DOI: 10.1063/1.3464263. Crossref, Web of Science, Google Scholar