Maximum violations of the quantum-witness equality

TL;DR

This paper derives an upper bound for violations of the quantum witness equality, linking it to measurement outcomes and showing quantum mechanics can reach this bound in large systems.

Contribution

It introduces a new upper bound for quantum witness violations based on measurement outcomes and connects it to trace distance between states.

Findings

Quantum mechanics can saturate the algebraic bound for large systems.

The upper bound depends only on the number of measurement outcomes.

A connection between quantum witness violations and trace distance is established.

Abstract

We consider the quantum witness test of macroscopic realism and derive an upper bound for possible violations of this equality due to quantum mechanics. The bound depends only on the number of possible outcomes for the blind measurement at the heart of the witness protocol. Mirroring recent results for the related Leggett-Garg inequality, we show that quantum mechanics can saturate the algebraic bound for large systems. We also establish a connection between the quantum witness and the trace distance between density matrices.