Shiladitya Mal

Temporal correlations and device-independent randomness

Leggett–Garg inequalities (LGI) are constraints on certain combinations of temporal correlations obtained by measuring one and the same system at two different instants of time. The usual derivations of LGI assume macroscopic realism per se and noninvasive measurability. We derive these inequalities under a different set of assumptions, namely the assumptions of predictability and no signaling in time (NSIT). As a novel implication of this derivation, we find application of LGI in randomness certification. It turns out that randomness can be certified from temporal correlations, even without knowing the details of the experimental devices, provided the observed correlations violate LGI but satisfy NSIT.

Optimal violation of the Leggett–Garg inequality for arbitrary spin and emergence of classicality through unsharp measurements

Abstract In the context of temporal correlations of particles with arbitrary spin, we obtain optimal violation of the Leggett–Garg inequality (LGI), improving upon an earlier result (Kofler, 2007 [24] ). Our proof is accomplished through a suitable adaptation of a measurement scheme, previously employed for studying spatial correlations. We next consider unsharp measurements as a method of coarse graining, and show that LGI can not be violated below a precise value of the sharpness parameter. We then apply Fines theorem in the context of LGI and derive a sufficient condition for emergence of classicality.

Quantum mechanical violation of macrorealism for large spin and its robustness against coarse-grained measurements

For multilevel spin systems, robustness of the quantum mechanical (QM) violation of macrorealism (MR) with respect to coarse-grained measurements is investigated using three different necessary conditions of MR, namely, the Leggett-Garg inequality (LGI), Wigners form of the Leggett-Garg inequality (WLGI), and the condition of no-signaling in time (NSIT). It is shown that for dichotomic sharp measurements, in the asymptotic limit of spin, the algebraic maxima of the QM violations of all these three necessary conditions of MR are attained. Importantly, the QM violations of all these persist in that limit even for arbitrary unsharp measurements, i.e., for any nonzero value of the sharpness parameter characterizing the degree of fuzziness of the relevant measurements. We also find that, when different measurement outcomes are clubbed into two groups for the sake of dichotomizing the outcomes, the asymmetry or symmetry in the number of outcomes in the two groups, signifying the degree of coarse graining of measurements, has a crucial role in discerning quantum violation of MR. The results clearly demonstrate that classicality does not emerge in the asymptotic limit of spin, whatever be the unsharpness and degree of coarse graining of the measurements.

Testing local-realism and macro-realism under generalized dichotomic measurements

Generalised quantum measurements with two outcomes are fully characterised by two real parameters, dubbed as sharpness parameter and biasedness parameter and they can be linked with different aspects of the experimental set up. It is known that precision of measurements, characterised by the sharpness parameter of the measurements, reduces the possibility of probing quantum features like violation of localrealism (LR) or macrorealism (MR). Here we investigate the effect of biasedness together with sharpness of measurement and find a trade-off between those two parameters in the context of probing violation of LR and MR. Interestingly we also find the above mentioned trade-off is more robust in the later case.