Exploring quantum foundations by NMR: Quantum correlations and measurements

Abstract

Research into quantum information and quantum computation has raised many fundamental questions. To make progress, a critical understanding of the fundamental aspects has become inevitable. Here we investigate, both experimentally and theoretically, some of the fundamental aspects of quantum mechanics viz., quantum contextuality, quantum measurement, quantum Fisher information, no-signaling principle, and quantum nonlocality.

Using a three qubit NMR register, we show that, quantum harmonic oscillator states exhibits quantum contextuality (i.e., no reality before measurement; in other words, we cannot assign values to observables even before measurement; measurement creates reality). Using a four qubit NMR register, we show that, NMR spectrometer is a Luders measuring device (which preserves superposition in the degenerate subspace corresponding to a degenerate observable being measured). Using a four qubit NMR star topology register (i.e., one central target qubit surrounded by three ancillary qubits), we show that, ancillary qubits pre-correlated with central target qubit, can amplify quantum Fisher information corresponding to the central target qubit (i.e., increases precision in unknown parameter estimation corresponding to the central target qubit).

Density matrix description is based on Kolmogorov's modern axiomatic probability measure theory of quantum random phenomena. However, in Kolmogorov's schema, a priori assumption of a constant value for the probability of a single random event is a purely mathematical quantity which is not motivated by experiment. Consequently, motivated by what we actually observe in experiments, we propose an alternative mathematical model wherein a priori probability measure is dropped completely and instead a posteriori limit-supremum of relative frequency is considered. We call the resulting theoretical model as the frequentist-inspired quantum mechanics wherein we consider the unknown quantum states path by path. Then we show that within the frequentist-inspired quantum mechanics, physically different ensembles described by the same density matrix are distinguishable via content dependent fluctuations.

Finally we show that, it is possible to violate Bell's inequality beyond Tsirelson bound by introducing context dependent unitary evolutions. Correct context dependency can be achieved by either post-selection or signaling. This leads to a more efficient quantum key distribution protocol.