Entangled states are not always useful for single shot distinguishability of unitaries

• URL: http://arxiv.org/abs/2504.14499v1
• Date: Sun, 20 Apr 2025 05:40:43 GMT
• Title: Entangled states are not always useful for single shot distinguishability of unitaries
• Authors: Satyaki Manna, Anandamay Das Bhowmik, Debashis Saha,
• Abstract summary: Two unitaries are distinguishable with non-maximally entangled state but indistinguishable with maximally entangled state.<n>One striking feature of optimal probing state in this task can be observed if we increase the number of unitaries more than two.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: There has been many instances where the entangled state as a probe acts better than the single state in the task of distinguishing quantum channels. We provide a proof in the agreement of this motion in the context of single shot distinguishability of two unitaries. But interestingly, there exists two unitaries which are distinguishable with non-maximally entangled state but indistinguishable with maximally entangled state. One striking feature of optimal probing state in this task can be observed if we increase the number of unitaries more than two. There exists a class of unitaries in every dimension $\geqslant$ 3 for which an input entangled state cannot distinguish them but an input single state can.

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