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One-way LOCC indistinguishable lattice states via operator structures

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Abstract

Lattice states are a class of quantum states that naturally generalize the fundamental set of Bell states. We apply recent results from quantum error correction and from one-way local operations and classical communication (LOCC) theory that are built on the structure theory of operator systems and operator algebras, to develop a technique for the construction of relatively small sets of lattice states not distinguishable by one-way LOCC schemes. We also present examples, show the construction extends to generalized Pauli states, and compare the construction to other recent work.

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Acknowledgements

D.W.K. was partly supported by NSERC and a University Research Chair at Guelph. C.M. was partly supported by a Mitacs Accelerate internship held with the African Institute for Mathematical Sciences (AIMS). R.P. was partly supported by NSERC. M.N. acknowledges the ongoing support of the Saint Mary’s College Office of Faculty Development and would like to thank Andrew Conner for helpful conversations.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of Guelph, Guelph, ON, N1G 2W1, Canada

    David W. Kribs, Comfort Mintah & Rajesh Pereira

  2. Institute for Quantum Computing and Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    David W. Kribs

  3. Department of Mathematics and Computer Science, Saint Mary’s College of California, Moraga, CA, 94556, USA

    Michael Nathanson

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  1. David W. Kribs
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  2. Comfort Mintah
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  4. Rajesh Pereira
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Correspondence to Comfort Mintah.

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Kribs, D.W., Mintah, C., Nathanson, M. et al. One-way LOCC indistinguishable lattice states via operator structures. Quantum Inf Process 19, 194 (2020). https://doi.org/10.1007/s11128-020-02686-6

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