Quantum measurement and pure dephasing

Abstract

The prerequisite of quantum measurement is a transformation of an initially off-diagonal density matrix ρmα;nβ describing an interacting measured object and measuring device into a diagonal density matrix ρmα;mαδmnδαβ . The latter density matrix describes a proper mixture of states having definitem-values. On the other hand, the irreversible relaxation (towards the thermodynamic equilibrium) is also characterized by transformation of an initially off-diagonal matrix into a diagonal one. It has been shown that the process of irreversible relaxation can be used to perform quantum measurement, provided the duration Δt of the measurement is much larger thanT 2, the phase relaxation time, and much smaller thanT 1, the population relaxation time:T 2 ≪ Δt ≪T 1. Agedanken experiment describing this kind of measurement is provided. Aπ/2-pulse transforms an initials z = −1/2 state into superposition ofs z = ±1/2 states. The irreversible relaxation leads to the proper mixture ofs z = 1/2 ands z = −1/2 state. Results of the measurements are verified by the second electromagnetic pulse.