Direct measurement of general quantum states using weak measurement

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.

This is a later and very different version of arXiv:1110.0727v3 [quant-ph]. New content: a method to directly measure each element of the density matrix, specific Hamiltonians to weakly measure the product of non-commuting observables, and references to recent related work

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