Estimation of Spin-Spin Interaction by Weak Measurement Scheme

Precisely knowing an interaction Hamiltonian is crucial to realize quantum information tasks, especially to experimentally demonstrate a quantum computer and a quantum memory. We propose a scheme to experimentally evaluate the spin-spin interaction for a two-qubit system by the weak measurement technique initiated by Yakir Aharonov and his colleagues. Furthermore, we numerically confirm our proposed scheme in a specific system of a nitrogen vacancy center in diamond. This means that the weak measurement can also be taken as a concrete example of the quantum process tomography.Comment: 4 pages, 1 table, 2 figures, to appear in Europhysics Letter

Complex joint probabilities as expressions of determinism in quantum mechanics

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the deterministic relation between the outcomes of different quantum measurements. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.Comment: 12 pages, including 1 figure, updated introduction includes references to the historical background of complex joint probabilities and to related work by Lars M. Johanse

Weak Values with Decoherence

The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a general framework of quantum operations to the W operator in parallel with the Kraus representation of the completely positive map for the density operator. The decoherence effect is also investigated in terms of the weak measurement by a shift of a probe wave function of continuous variable. As an application, we demonstrate how the geometric phase is affected by the bit flip noise.Comment: 17 pages, 3 figure

Geometrical aspects of weak measurements and quantum erasers

We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak measurement is achieved owing to the Pancharatnam phase associated with post-selection.Comment: 11 pages, 4 figure