I will describe theory and experiments with superconducting qubits revealing how a quantum gets from state A to state B, while being both measured and driven simultaneously. This most probable path may be found using a principle of least action.
The propagator plays a central role in path integral theory and therefore has significant value in various fields of modern quantum physics, where path integral representations can be used. However, owing to the fact that it has not been directly measured in experiment, progress of experimental studies of quantum systems based on path integral representations has been seriously limited. Recently, we proposed a propagator measurement scheme based on the direct measurement of the wave function and successfully performed the first experimental measurement of the propagator by using a single photon experiment. Furthermore, in this study, the quantum principle of least action is demonstrated for the first time. This research successfully addresses the technical challenges of path integral experimental studies. In this work, we review the research progress in this field, including a brief introduction to the basic concepts and research progress of direct wave function measurement, and a detailed description of the theoretical model, experimental design, and experimental results of propagator measurement. Finally, we introduce an important application example, which can serve as the experimental demonstration of the quantum principle of least action through propagator measurement. The research progress of propagator measurement reviewed in this work will provide important references for future experimental studies by using this method.
Protective measurements illustrate how Yakir Aharonov's fundamental insights into quantum theory yield new experimental paradigms that allow us to test quantum mechanics in ways that were not possible before. As for quantum theory itself, protective measurements demonstrate that a quantum state describes a single system, not only an ensemble of systems, and reveal a rich ontology in the quantum state of a single system. We discuss in what sense protective measurements anticipate the theorem of Pusey, Barrett, and Rudolph (PBR), stating that, if quantum predictions are correct, then two distinct quantum states cannot represent the same physical reality. Introduction Although protective measurements [1, 2] are a new tool for quantum theory and experiment, they have yet to find their way into the laboratory; also theorists have not put them to best use, beyond a 1993 paper by Anandan on “Protective measurement and quantum reality” [3]. In Section 10.2, we point out that protective measurements offer new experimental tests of quantum mechanics, and we review recent experiments attempting to measure quantum wave functions. In Section 10.3, we present the Pusey–Barrett–Rudolph (PBR) theorem and discuss their conclusion that the quantum state represents physical reality, and in Section 10.4, we discuss in what sense protective measurements anticipate this conclusion. Protective measurement: implications for experiment and theory In 1926, Schrödinger postulated his equation for “material waves” in analogy with light waves: paths of material particles – which obey the principle of least action – are an approximation to material waves, just as rays of light – which obey the principle of least time – are an approximation to light waves [4]. But Born soon discarded “the physical pictures of Schr00F6;dinger” [5] and gave the “material wave” Ψ ( x , t ) a new interpretation: | Ψ ( x , t )| 2 is the probability density to find a particle at x at time t . Even Schrödinger was obliged to accept Born's interpretation.
We present a unified variational framework that bridges the Harmonic–Prime Wave Theory (PWT) with the Minimum Spanning Tree (MST) least-action principle of the Malallah Unified Mesh Theory (MUT). MUT derives all fundamental physics from entangled virtual photon pairs, where quantum paths correspond to MSTs of the Bell-state graph, embodying the principle of least action [1]. We demonstrate that the prime-indexed harmonic field Ψ(n) constitutes the irreducible MST basis of the integer mesh. Composite frequencies introduce redundant cycles that increase the global action, while primes form the minimal independent set required to reconstruct arithmetic structure. We formulate a discrete action functional whose minimizers naturally localize on prime indices, consistent with MUT’s path-weight Born rule. After applying MUT’s lattice-regularized renormalization group running, the framework achieves compatibility with atomic-scale observables. We derive wave–particle duality and the uncertainty principle as emergent consequences of MST degeneracy breaking and buffer confinement. We further extend the framework to quark physics and quantum tunneling, showing that color SU (3), fractional charges, confinement, the mass hierarchy, and tunneling deviations emerge from prime-resonance ooblocks, MST path selection, and prime-harmonic phase matching. We provide rigorous proofs, convergence analysis, computational recipes, and experimental protocols, establishing VPMT as a testable, least-action-driven extension of MUT’s quantum mesh dynamics.