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- W3104209239 abstract "A set of $n$ pure quantum states is called antidististinguishable if there exists an $n$-outcome measurement that never outputs the outcome `$k$' on the $k$-th quantum state. We describe sets of quantum states for which any subset of three states is antidistinguishable and use this to produce a two-player communication task that can be solved with $log d$ qubits, but requires one-way communication of at least $log (4/3) (d-1) - 1 approx 0.415 (d-1) - 1$ classical bits. The advantages of the approach are that the proof is simple and self-contained -- not needing, for example, to rely on hard-to-establish prior results in combinatorics -- and that with slight modifications, non-trivial bounds can be established in any dimension $geq 3$. The task can be framed in terms of the separated parties solving a relation, and the separation is also robust to multiplicative error in the output probabilities. We show, however, that for this particular task, the separation disappears if two-way classical communication is allowed. Finally, we state a conjecture regarding antidistinguishability of sets of states, and provide some supporting numerical evidence. If the conjecture holds, then there is a two-player communication task that can be solved with $log d$ qubits, but requires one-way communication of $Omega (d log d)$ classical bits." @default.
- W3104209239 created "2020-11-23" @default.
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- W3104209239 date "2020-03-17" @default.
- W3104209239 modified "2023-10-13" @default.
- W3104209239 title "Simple communication complexity separation from quantum state antidistinguishability" @default.
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- W3104209239 doi "https://doi.org/10.1103/physrevresearch.2.013326" @default.
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