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arXiv · 2406.08360

Operational Interpretation of the Choi Rank Through k-State Exclusion

Benjamin Stratton·Chung-Yun Hsieh·Paul Skrzypczyk
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Abstract

The Choi-state is an indispensable tool in the study and analysis of quantum channels. Considering a channel in terms of its associated Choi-state can greatly simplify problems. It also offers an alternative approach to the characterisation of a channel, with properties of the Choi-state providing novel insight into a channel's behaviour. The rank of a Choi-state, termed the Choi-rank, has proven to be an important characterising property, and here, its significance is further elucidated through an operational interpretation. The Choi-rank is shown to provide a universal bound on how successfully two agents, Alice and Bob, can perform an entanglement-assisted exclusion task. The task can be considered an extension of super-dense coding, where Bob can only output information about Alice's encoded bit-string with certainty. Conclusive state exclusion, in place of state discrimination, is therefore considered at the culmination of the super-dense coding protocol. In order to prove this result, a necessary condition for conclusive k-state exclusion of a set of states is presented in order to achieve this result, and the notions of weak and strong exclusion are introduced.

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Benjamin Stratton, Chung-Yun Hsieh, Paul Skrzypczyk. 2024-06-12. Operational Interpretation of the Choi Rank Through k-State Exclusion. https://doi.org/10.1103/physreva.110.l050601

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