"Correlation as a Resource in Unitary Quantum Mechanics and Its Application"

Abstract:

Quantum measurement results in objective, redundant, classical records. In unitary quantum mechanics, the environment plays a crucial role in creating these records. What structure must a quantum environment possess for unitary quantum measurement to produce such records?

Requiring measurement-outcome-conditional environment branches to be perfectly distinguishable, we show that the measurement unitaries must satisfy the Knill–Laflamme conditions of quantum error correction: the admissible initial environments form a code subspace, and the post-measurement subspace factorises into a pointer factor carrying the outcome and a memory factor retaining the environment's prior information.

Using the concept of Objective Classical Reality, we derive a dimension count that bounds the achievable redundancy of the measured outcome. A smaller code subspace for the environment permits more redundant records. This pointer-basis agreement among fragments is interpreted as a basis-dependent and finite resource that the measurement dynamics consumes to build redundant records.

We describe the formation of classical records and discuss an application of this mode of thinking in the context of locality in quantum mechanics.