Mixed state geometric phases, entangled systems, and local unitary transformations

M Ericsson, A K Pati, E Sjoqvist, J Brannlund, D K L Oi

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.

LanguageEnglish
Article number090405
Pages-
Number of pages4
JournalPhysical Review Letters
Volume91
Issue number9
DOIs
Publication statusPublished - 29 Aug 2003

Fingerprint

geometry
Hilbert space
interferometry

Keywords

  • quantum systems
  • parallel transport
  • interferometry

Cite this

Ericsson, M ; Pati, A K ; Sjoqvist, E ; Brannlund, J ; Oi, D K L . / Mixed state geometric phases, entangled systems, and local unitary transformations. In: Physical Review Letters. 2003 ; Vol. 91, No. 9. pp. -.
@article{2d2e58c43146449e89b5e70ea673cd18,
title = "Mixed state geometric phases, entangled systems, and local unitary transformations",
abstract = "The geometric phase for a pure quantal state undergoing an arbitrary evolution is a {"}memory{"} of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.",
keywords = "quantum systems, parallel transport, interferometry",
author = "M Ericsson and Pati, {A K} and E Sjoqvist and J Brannlund and Oi, {D K L}",
year = "2003",
month = "8",
day = "29",
doi = "10.1103/PhysRevLett.91.090405",
language = "English",
volume = "91",
pages = "--",
journal = "Physical Review Letters",
issn = "0031-9007",
number = "9",

}

Mixed state geometric phases, entangled systems, and local unitary transformations. / Ericsson, M ; Pati, A K ; Sjoqvist, E ; Brannlund, J ; Oi, D K L .

In: Physical Review Letters, Vol. 91, No. 9, 090405, 29.08.2003, p. -.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Mixed state geometric phases, entangled systems, and local unitary transformations

AU - Ericsson, M

AU - Pati, A K

AU - Sjoqvist, E

AU - Brannlund, J

AU - Oi, D K L

PY - 2003/8/29

Y1 - 2003/8/29

N2 - The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.

AB - The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.

KW - quantum systems

KW - parallel transport

KW - interferometry

UR - http://arxiv.org/PS_cache/quant-ph/pdf/0206/0206063v2.pdf

U2 - 10.1103/PhysRevLett.91.090405

DO - 10.1103/PhysRevLett.91.090405

M3 - Article

VL - 91

SP - -

JO - Physical Review Letters

T2 - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 9

M1 - 090405

ER -