Operational Quantum Average-Case Distances

• DOI: 10.22331/q-2023-09-11-1106
• Publication Date: 2023-09-11T12:37:32Z
• Authors: Filip B. Maciejewski; Zbigniew Puchała; Michał Oszmaniec
• Keywords: Trace distance; Statistical distance; TRACE (psycholinguistics)

We introduce distance measures between quantum states, measurements, and channels based on their statistical distinguishability in generic experiments. Specifically, we analyze the average Total Variation Distance (TVD) output statistics of protocols which objects are intertwined with random circuits measured standard basis. show that for forming approximate 4-designs, TVDs can be approximated by simple explicit functions underlying – average-case distances (ACDs). apply them to effects noise advantage experiments efficient discrimination high-dimensional states without memory. argue ACDs better suited assessing quality NISQ devices than common such as trace or diamond norm.