Direct measurement of general quantum states using weak measurement

TL;DR

This paper extends the direct measurement technique to mixed quantum states by using weak measurements of observable products, enabling in situ determination of the density matrix without destroying the state.

Contribution

It generalizes the previous wavefunction measurement method to mixed states through weak measurement of observable products, providing an operational way to directly measure the density matrix.

Findings

Allows direct measurement of mixed states

Requires only two basis measurements

Can be performed in situ without destroying the state

Abstract

Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed `in situ', determining the quantum state without destroying it.