Unitary holonomies by direct degenerate projections

Research output: Contribution to journalArticle

1 Citation (Scopus)
76 Downloads (Pure)

Abstract

An incomplete quantum measurement can induce non-trivial dynamics between degenerate subspaces, a closed sequence of such projections produces a non-abelian holonomy. We show how to induce unitary evolution on an initial subspace from such finite discrete sequences and also construct a near deterministic repeat-until-success protocol. We also prove necessary and sufficient criteria on the auxiliary Hilbert space dimension required for inducing isometries between between subspaces.
Original languageEnglish
Article number050102(R)
Number of pages4
JournalPhysical Review A
Volume89
DOIs
Publication statusPublished - 15 May 2014

Fingerprint

Hilbert space
projection

Keywords

  • unitary holonomies
  • direct degenerate projections
  • non-abelian holonomy
  • isometries
  • Hilbert dimension

Cite this

@article{e1080de8485f46e49187c1cb05d3e50d,
title = "Unitary holonomies by direct degenerate projections",
abstract = "An incomplete quantum measurement can induce non-trivial dynamics between degenerate subspaces, a closed sequence of such projections produces a non-abelian holonomy. We show how to induce unitary evolution on an initial subspace from such finite discrete sequences and also construct a near deterministic repeat-until-success protocol. We also prove necessary and sufficient criteria on the auxiliary Hilbert space dimension required for inducing isometries between between subspaces.",
keywords = "unitary holonomies, direct degenerate projections, non-abelian holonomy, isometries, Hilbert dimension",
author = "Oi, {Daniel K.L.}",
year = "2014",
month = "5",
day = "15",
doi = "10.1103/PhysRevA.89.050102",
language = "English",
volume = "89",
journal = "Physical Review A - Atomic, Molecular, and Optical Physics",
issn = "1050-2947",

}

Unitary holonomies by direct degenerate projections. / Oi, Daniel K.L.

In: Physical Review A, Vol. 89, 050102(R), 15.05.2014.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Unitary holonomies by direct degenerate projections

AU - Oi, Daniel K.L.

PY - 2014/5/15

Y1 - 2014/5/15

N2 - An incomplete quantum measurement can induce non-trivial dynamics between degenerate subspaces, a closed sequence of such projections produces a non-abelian holonomy. We show how to induce unitary evolution on an initial subspace from such finite discrete sequences and also construct a near deterministic repeat-until-success protocol. We also prove necessary and sufficient criteria on the auxiliary Hilbert space dimension required for inducing isometries between between subspaces.

AB - An incomplete quantum measurement can induce non-trivial dynamics between degenerate subspaces, a closed sequence of such projections produces a non-abelian holonomy. We show how to induce unitary evolution on an initial subspace from such finite discrete sequences and also construct a near deterministic repeat-until-success protocol. We also prove necessary and sufficient criteria on the auxiliary Hilbert space dimension required for inducing isometries between between subspaces.

KW - unitary holonomies

KW - direct degenerate projections

KW - non-abelian holonomy

KW - isometries

KW - Hilbert dimension

UR - http://journals.aps.org/pra/

U2 - 10.1103/PhysRevA.89.050102

DO - 10.1103/PhysRevA.89.050102

M3 - Article

VL - 89

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

M1 - 050102(R)

ER -