Reconstruction of quantum states of spin systems: From quantum Bayesian inference to quantum tomography
This paper studies a posteriori estimation schemes of the state of a quantum mechanical system (represented by a density operator) based on measurement data. The paper centres around and analyzes the connection between reconstruction schemes based on (i) quantum Bayesian inference, (ii) Jaynes principle of maximum entropy and (iii) quantum tomography (i.e., the complete reconstruction of the initial quantum state from the measurement data). The reconstruction scheme (iii) can only be applied in situations where all system observables are precisely measured and the scheme (ii) only in situations where part of the system observables are precisely measured whereas quantum Bayesian inference can be applied unambiguously only if the state of the quantum system is a priori known to be pure. The authors argue that a posteriori estimation of mixed quantum states via the quantum Bayesian inference is possible by viewing the quantum system described by the mixed state as a part of a larger composed system which is in a pure state and by taking up the point of view that impurity arises as a consequence of the fact that the system under consideration is entangled with another system. The examples of a single spin-1/2 system and of two spin-1/2 systems are discussed in great detail. The authors demonstrate that in the limit of a large number of measurements the Bayesian inference method gives the same result as the Jaynes principle of maximum entropy. Another discussed issue is the detection of quantum entanglement between two spin \(1/2\) systems from incomplete measurement data.
scientific article; zbMATH DE number 1275051