Maximal gap between local and global distinguishability of bipartite quantum states

• URL: http://arxiv.org/abs/2110.04387v1
• Date: Fri, 8 Oct 2021 21:40:02 GMT
• Title: Maximal gap between local and global distinguishability of bipartite quantum states
• Authors: Willian H. G. Corr\^ea, Ludovico Lami, Carlos Palazuelos
• Abstract summary: We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states.
• Score: 7.605814048051737
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two orthogonal quantum states of a $n_A\times n_B$ bipartite quantum system can be discriminated via local measurements with an error probability no larger than $\frac12 \left(1 - \frac{1}{c \min\{n_A, n_B\}} \right)$, where $1\leq c\leq 2\sqrt2$ is a universal constant, and our bound scales provably optimally with the local dimensions $n_A,n_B$. Mathematically, this is achieved by showing that the distinguishability norm $\|\cdot\|_{LO}$ associated with local measurements satisfies that $\|\cdot\|_1\leq 2\sqrt2 \min\{n_A,n_B\} \|\cdot\|_{LO}$, where $\|\cdot\|_1$ is the trace norm.

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