Interferometrically estimating a quadratic form for any immanant of a matrix and its permutations

Aeysha Khalique, Hubert de Guise, and Barry C. Sanders
Phys. Rev. A 101, 052314 – Published 7 May 2020

Abstract

We devise a multiphoton interferometry scheme for sampling a quadratic function of a specific immanant for any submatrix of a unitary matrix and its row permutations. The full unitary matrix describes a passive, linear interferometer, and its submatrix is used when photons enter in and are detected at subsets of possible input and output channels. Immanants are mathematical constructs that interpolate between the permanent and determinant; contrary to determinants and permanents, which have meaningful physical applications, immanants are devoid of physical meaning classically but here are shown to be meaningful in a quantum setting. Our quadratic form of immanants is sampled by injecting vacuum and single photons into interferometer input ports such that the photon arrival times are entangled, in contrast to previous methods that control arrival times without entangling. Our method works for any number of photons, and we solve explicitly the quadratic form for the two-, three-, and four-photon cases.

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  • Received 9 July 2019
  • Revised 24 January 2020
  • Accepted 23 March 2020

DOI:https://doi.org/10.1103/PhysRevA.101.052314

©2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Aeysha Khalique1,2, Hubert de Guise3,*, and Barry C. Sanders4,5,†

  • 1School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan
  • 2National Centre for Physics (NCP), Shahdra Valley Road, Islamabad 44000, Pakistan
  • 3Department of Physics, Lakehead University, Thunder Bay, Ontario P7B 5E1, Canada
  • 4Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada
  • 5Program in Quantum Information Science, Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada

  • *hubert.deguise@lakeheadu.ca
  • sandersb@ucalgary.ca

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Vol. 101, Iss. 5 — May 2020

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