Macroscopic instructions vs microscopic operations in quantum circuits

TL;DR

This paper investigates whether macroscopic instructions in quantum experiments produce consistent microscopic operations, introduces tests for detecting context-dependence, and provides tools to measure the unitarity and state accessibility of quantum operations.

Contribution

It develops practical, non-tomographic tests for detecting context-dependence in quantum operations and introduces measures for unitarity and state volume estimation.

Findings

Tests can detect context-dependence without full tomography.

Methods are robust to experimental imperfections.

Tools for quantifying unitarity and state accessibility are proposed.

Abstract

In many experiments on microscopic quantum systems, it is implicitly assumed that when a macroscopic procedure or "instruction" is repeated many times -- perhaps in different contexts -- each application results in the same microscopic quantum operation. But in practice, the microscopic effect of a single macroscopic instruction can easily depend on its context. If undetected, this can lead to unexpected behavior and unreliable results. Here, we design and analyze several tests to detect context-dependence. They are based on invariants of matrix products, and while they can be as data intensive as quantum process tomography, they do not require tomographic reconstruction, and are insensitive to imperfect knowledge about the experiments. We also construct a measure of how unitary (reversible) an operation is, and show how to estimate the volume of physical states accessible by a quantum operation.