Quantum Coherence, Classical Limit and Temporal Bell Inequalities

Tommaso Calarco, Roberto Onofrio

Tommaso Calarco

G. Waldherr, Philipp Neumann, Susana F. Huelga +2 more

Quantum nonlocality has been experimentally investigated by testing different forms of Bell's inequality, yet a loophole-free realization has not been achieved up to now. Much less explored are temporal Bell inequalities, which are not subject to the locality assumption, but impose a constraint on the system's time correlations. In this Letter, we report on the experimental violation of a temporal Bell's inequality using a nitrogen-vacancy (NV) defect in diamond and provide a novel quantitative test of quantum coherence. Such a test requires strong control over the system, and we present a new technique to initialize the electronic state of the NV with high fidelity, a necessary requirement also for reliable quantum information processing and/or the implementation of protocols for quantum metrology.

Lawrence J. Landau

Fumiaki Morikoshi

An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality is an immediate consequence of the quantumness in the computation. Furthermore, this approach suggests a notion of temporal nonlocality in quantum computation.

Aurindam Mondal

We investigate the role of the bipartite temporal Bell inequality, an analogue of the spatial Bell inequality, in probing the quantum imprints of primordial perturbations when the initially chosen Bunch-Davies vacuum is replaced by a coherent state. Although it is based on the same principles of locality and realism, its primary advantage lies in the fact that it does not require two distinct set of observable for its construction. Instead, measurements performed on a single component of the pseudo-spin operator at different times are sufficient. Consequently, it is particularly well suited for cosmological scenarios, where observational constraints typically allow access to only one component of the pseudo-spin operator. Assuming a coherent state as the initial condition, we derive an analytical expression for the expectation value of the bipartite temporal Bell operator and demonstrate the absence of temporal Bell violation in such a scenario. Interestingly, the results for squeezed coherent state is found to differ - albeit slightly - from those of squeezed vacuum state for large values of the squeezing parameter. This suggests that the ability to distinguish among different initial states of primordial perturbations does not rely on the violation of temporal Bell inequality. Furthermore, the dependence of the temporal Bell inequality on a purely imaginary phase factor of the wave function appears to be an unique feature, which is entirely absent in the context of spatial Bell inequalities.