Quantum measurement in the charge representation

TL;DR

This paper develops a theoretical framework for analyzing charge transfer statistics in quantum systems, enabling joint measurement evaluation and exploring conditions for projective quantum measurements in a point contact setup.

Contribution

It introduces a charge-specific density matrix approach and derives a master equation for charge transfer in a tunneling model, advancing quantum measurement theory.

Findings

Charge transfer statistics can be described using a charge-specific density matrix.

Conditions for projective measurements are identified in the presence of Nyquist or Schottky noise.

The theory applies to two-state quantum systems, providing insights into measurement dynamics.

Abstract

Counting statistics of charge transfers in a point contact interacting with an arbitrary quantum system is studied. The theory for the charge specific density matrix is developed, allowing the evaluation of the probability of the outcome of any joint measurement of the state of the quantum system and the transferred charge. Applying the method of charge projectors, the master equation for the charge specific density matrix is derived in the tunneling Hamiltonian model of the point contact. As an example, the theory is applied to a quantum measurement of a two-state system: The evolution of the charge specific density matrix in the presence of Nyquist or Schottky noise is studied and the conditions for the realization of a projective measurement are established.