Quantum Physics

The state vector describing the physical situation of the magnetic A-B effect should depend upon all three quantizeable entities in the problem, the electron orbiting the solenoid, the moving charged particles in the solenoid and the vector potential. One may imagine three approximate solutions to the exact dynamics, where two of the three entities do not interact at all, and the third, quantized, entity interacts with a classical approximation. Thus, fifty-five years ago, A-B showed that, if the interaction is between the quantized electron current and the classical approximation to the solenoid’s vector potential, the state vector acquires a measurable phase shift. Four years ago Vaidman showed that, if the interaction is between the quantized solenoid current and the classical approximation to the electron’s vector potential, the state vector acquires the A-B phase shift. I shall first show why these two results have to be the same. Then, I shall show that, if the interaction is between the quantized vector potential and the classical approximation to the electron and solenoid currents, the state vector acquires the A-B phase shift. Lastly, I shall show how to reconcile these three mathematically and conceptually different calculations.

In this brief talk we will show how weak values appear in a wide range of physical contexts beyond the usual context of weak measurements. Among others, we will discuss how weak values appear in: the physics of classical parameters in a quantum evolution; the statistics of strong measurements; formulas for probability amplitudes in quantum mechanics; and finally, in the classical correspondence of quantum mechanics.

Phase space methods are ubiquitous in quantum mechanics. From the Weyl-Wigner Moyal formalism to coherent states and discrete phase spaces we see the imprints of the classical world again and again. In this presentation, we address one of two major developments introduced by Aharonov and his collaborators: The concept of weak values that stems from a time-symmetric view of quantum physics. We look at the weak measurement through two distinct geometric frames: The geometry of the measuring apparatus and the geometry of the measured system. We …nalize with some brief comments on the second major conceptual due to Aharonov and collaborators: the theory of modular variables and how Schwinger´s discrete phase space structure helps to shed light on it. We conclude then with the following mantra: It´ s all about phase space.

In classical mechanics, an action is defined only modulo additive terms which do not modify the equations of motion; in certain cases, these terms are topological quantities. We construct an infinite sequence of higher order topological actions and argue that they play a role in quantum mechanics, and hence can be accessed experimentally.

Curiosity about how the world works can lead to beneficial progress in technology, and vice-versa. This kind of interplay can be found in quantum nanoscience, where foundationally motivated experiments and technologically motivated experiments often use similar materials and techniques, because both involve extending the realm of non-classical behaviour. At a higher level, curiosity about ultimate questions such as meaning and purpose can create an environment that is conducive to scientific breakthroughs, and many of the best minds in science have also been curious about deeper realities. Eugene Wigner described the miracle of the effectiveness of mathematics as a wonderful gift which we neither understand nor deserve. The same could be said of curiosity.

Superconducting circuit technology has rapidly developed over the past several years to become a leading contender for realizing a scalable quantum computer. Modern circuit designs are based on the transmon qubit, which coherently superposes macroscopic charge oscillations. Measurements of a transmon are fundamentally weak and continuous in time, with projective measurements emerging only after a finite duration. Adding gates, such measurements may then implement ancilla-based measurements of controllable strength. Recent experiments have used both types of weak measurement to great effect: for monitoring qubit evolution, and for showing violations of a hybrid Bell-Leggett-Garg inequality.

The Kochen-Specker (KS) theorem can gives rise to logical paradoxes under pre- and post-selection in which the contextual behavior is confined to specific observables of a system. Weak measurements allow direct experimental observation of the nonclassical behavior of these specific observables. This presents an experimental advantage over other tests of KS inequalities which rule out a particular class of counterfactual noncontextual hidden variable models, but can never specify where the contradiction occurs, nor make any direct observation of its consequences. The confined contextuality can always be interpreted as a logical pre- and post-selection paradox, such as the 3-box paradox, the Quantum Cheshire Cat, or the Quantum Pigeonhole Effect. This confined contextuality was recently observed using neutron inferometry for KS sets of up to 17 qubits. Details of the theory and experimental results will be presented.