Invariant measures on multimode quantum Gaussian states

被引：10

作者：

Lupo, C. ^{[1
]}

Mancini, S. ^{[1
,2
]}

De Pasquale, A. ^{[3
,4
]}

Facchi, P. ^{[5
,6
,7
]}

Florio, G. ^{[7
,8
,9
,10
,11
]}

Pascazio, S. ^{[7
,8
,9
]}

机构：

[1] Univ Camerino, Sch Sci & Technol, I-62032 Camerino, Italy

[2] Ist Nazl Fis Nucl, Sez Perugia, I-06123 Perugia, Italy

[3] Scuola Normale Super Pisa, NEST, I-56126 Pisa, Italy

[4] Ist Nanosci CNR, I-56126 Pisa, Italy

[5] Univ Bari, Dipartimento Matemat, I-70125 Bari, Italy

[6] Univ Bari, MECENAS, I-70125 Bari, Italy

[7] Ist Nazl Fis Nucl, Sez Bari, I-70126 Bari, Italy

[8] Univ Bari, MECENAS, I-70126 Bari, Italy

[9] Univ Bari, Dipartimento Fis, I-70126 Bari, Italy

[10] Museo Stor Fis, I-00184 Rome, Italy

[11] Ctr Studi & Ric Enrico Fermi, I-00184 Rome, Italy

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2012年 / 53卷 / 12期

关键词：

TYPICAL ENTANGLEMENT; COHERENT STATES; PURE STATES; ENTROPY; REPRESENTATION; INFORMATION; MECHANICS; SYSTEMS; FORMS;

D O I：

10.1063/1.4768712

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4768712]

引用

页数：19

共 37 条

[1] Generic entanglement and standard form for N-mode pure Gaussian states [J].

Adesso, Gerardo .

PHYSICAL REVIEW LETTERS, 2006, 97 (13)

[2] ENTROPY, WIGNER DISTRIBUTION FUNCTION, AND APPROACH TO EQUILIBRIUM OF A SYSTEM OF COUPLED HARMONIC OSCILLATORS [J].

AGARWAL, GS .

PHYSICAL REVIEW A, 1971, 3 (02) :828-&

[3] Exploring representation theory of unitary groups via linear optical passive devices [J].

Aniello, P. ;

Lupo, C. ;

Napolitano, M. .

OPEN SYSTEMS & INFORMATION DYNAMICS, 2006, 13 (04) :415-426

[4] Modewise entanglement of Gaussian states [J].

Botero, A ;

Reznik, B .

PHYSICAL REVIEW A, 2003, 67 (05) :5

[5] Optimized generation of heralded Fock states using parametric down-conversion [J].

Branczyk, Agata M. ;

Ralph, T. C. ;

Helwig, Wolfram ;

Silberhorn, Christine .

NEW JOURNAL OF PHYSICS, 2010, 12

[6] Quantum information with continuous variables [J].

Braunstein, SL ;

van Loock, P .

REVIEWS OF MODERN PHYSICS, 2005, 77 (02) :513-577

[7] The emergence of typical entanglement in two-party random processes [J].

Dahlsten, O. C. O. ;

Oliveira, R. ;

Plenio, M. B. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2007, 40 (28) :8081-8108

[8] Statistical distribution of the local purity in a large quantum system [J].

De Pasquale, A. ;

Facchi, P. ;

Giovannetti, V. ;

Parisi, G. ;

Pascazio, S. ;

Scardicchio, A. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (01)

[9] Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system [J].

De Pasquale, A. ;

Facchi, P. ;

Parisi, G. ;

Pascazio, S. ;

Scardicchio, A. .

PHYSICAL REVIEW A, 2010, 81 (05)

[10] Phase transitions of bipartite entanglement [J].

Facchi, P. ;

Marzolino, U. ;

Parisi, G. ;

Pascazio, S. ;

Scardicchio, A. .

PHYSICAL REVIEW LETTERS, 2008, 101 (05)

← 1 2 3 4 →