Discriminating between L\"uders and von Neumann measuring devices: An NMR investigation

TL;DR

This paper experimentally distinguishes between L"uders and von Neumann measurement rules in quantum systems using NMR, confirming that L"uders rule better describes the measurement process in degenerate cases.

Contribution

The study reformulates a protocol to discriminate measurement devices and experimentally tests it with NMR, favoring L"uders rule in quantum measurements.

Findings

L"uders rule is favored over von Neumann rule in the experiments.

The protocol was successfully adapted for quantum registers with system and ancilla qubits.

NMR techniques effectively demonstrated the discrimination between measurement rules.

Abstract

Measurement of an observable on a quantum system involves a probabilistic collapse of the quantum state and a corresponding measurement outcome. L\"uders and von Neumann state update rules attempt to describe the above phenomenological observations. These rules are identical for a nondegenerate observable, but differ for a degenerate observable. While L\"uders rule preserves superpositions within a degenerate subspace under a measurement of the corresponding degenerate observable, the von Neumann rule does not. Recently Hegerfeldt and Mayato [Phys. Rev. A, 85, 032116 (2012)] had formulated a protocol to discriminate between the two types of measuring devices. Here we have reformulated this protocol for quantum registers comprising of system and ancilla qubits. We then experimentally investigated this protocol using nulear spin systems with the help of NMR techniques, and found that L\"uders rule is favoured.