Measuring polynomial invariants of multiparty quantum states

M. S. Leifer, N. Linden, and A. Winter
Phys. Rev. A 69, 052304 – Published 7 May 2004

Abstract

We present networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our networks can estimate the LU invariants for multiparty states, where each party can have a Hilbert space of arbitrary dimension and the SLOCC invariants for multiqubit states. We analyze the statistical efficiency of our networks compared to methods based on estimating the state coefficients and calculating the invariants.

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  • Received 15 August 2003

DOI:https://doi.org/10.1103/PhysRevA.69.052304

©2004 American Physical Society

Authors & Affiliations

M. S. Leifer* and N. Linden

  • Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom

A. Winter

  • Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom

  • *Present address: Perimeter Institute for Theoretical Physics, 35 King Street North, Waterloo, Ontario, N2J 2W9, Canada. Email address: mleifer@perimeterinstitute.ca
  • Present address: Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom.

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Issue

Vol. 69, Iss. 5 — May 2004

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