Quantum Foundations

There is a common framework for the measurement problem for sensors such as radars, sonars, and optics in a common language by casting analysis of signals in the language of quantum mechanics (Rigged Hilbert Space). The use of this language can reveal a more detailed understanding of the underlying interactions of a return signal that are not usually brought out by standard signal processing design techniques. The weak measurement Ansatz first provided by the Aharonov, Albert and Vaidman paper (A2V) that introduced weak values to the world provides an explicit means to consider all interactions of a signal with an object by using what we term the Aharonov Ansatz. The Aharonov Ansatz for sensing can summarized as: 1. Any sensor measurement process, whether active or passive can be thought of as determining the mathematical operator's characteristics of a signal's interaction with a object. 2. Certain types of interaction operators can be "post-selected" for in the return signal when the broadcast signal is known for either a single or multiple operators so receiver design can be optimized. 3. In principle detectors can design can be optimized, "matched" to signal interaction for these operators (operator matched filter), so mathematical solutions to receiver (in the classical sense) design or the design of apparatus of difficult to measure quantum interactions can be improved as has been reported in the literature. 4. Matching or post-selection to a given operator, when possible, maximizes ability to detect a "signal" or the characteristics of an interaction. Finally, in this talk we note a connection between this work and a the variational functional used in perturbation theory in quantum mechanics.

In 2005 R. Spekkens presented a generalization of noncontextuality that applies to imperfect measurements (POVMs) by allowing the underlying ontological model to be indeterministic. Unlike traditional Bell-Kochen-Specker noncontextuality, ontological models of a single qubit were shown to be contextual under this definition. Recently, M. Pusey showed that, under certain conditions, exhibiting an anomalous weak value implies contextuality. We will present a single qubit prepare and measure QKD protocol that uses observation of anomalous weak values of particular observables to estimate the quantum channel error rate and certify the security of the channel. We will also argue that it is the “degree” of contextuality of the noisy qubits exiting the channel that fundamentally determine the secure key rate. A benefit of this approach is that the security does not depend on the fair sampling assumption, and so is not compromised by Eve controlling Bob’s measurement devices. Thus it retains much of the benefit of “Measurement Device Independent” QKD protocols while only using single photon preparation and measurement.

Measurements performed at variable strengths show that non-commuting physical properties are related by complex-valued statistics, where the complex phase expresses the action of transformations along orbits represented by the eigenstates. In strong measurements, the dynamics along the orbits is completely randomized, which means that the pure states prepared by such a measurement actually represent ergodic statistics where the coherence between components originates from quantum dynamics. The complex algebra of Hilbert space inner products describes the intersection of two ergodically randomized orbits, where the complex phase describes the action of propagation along the orbits. Since the same action also appears in classical descriptions of the dynamics it is possible to derive quantum states and their time evolution directly from the classical equations of motion, without the abstractions of operator algebra. A representative example of this fundamental relation between classical dynamics and quantum coherence is the multi-photon interference in two-path interferometers, where the multi-photon interference fringes can be explained by the action enclosed by two classical orbits corresponding to the input and output photon number states. This example shows how the non-classical features of quantum statistics emerge from the effects of enclosed actions on the causality relations between the initial orbit prepared by ergodic randomization and the final orbit along which the system was sampled during the measurement. Since action relations take the same form in quantum mechanics and in the classical limit, any attempt to explain quantum mechanics should start with an analysis of the dynamics. The conventional sense of reality only emerges from the consistency of causality relations,not from any abstract ``knowledge of reality''. Our concepts of particles and trajectories only have an approximate validity which breaks down in the limit of small action. Reality always requires the dynamics of interaction, and hbar is an absolute limitation of physical reality. In this presentation, I hope to clarify that this absence of a microscopic material reality can be understood quite naturally in terms of the well known physics of dynamics and interactions, removing the need for any untestable platonic assumptions about a hypothetical ``reality out there''.

Peculiarities of quantum mechanical predictions on a fundamental level are investigated intensively in matter-wave optical setups; in particular, neutron interferometric strategy has been providing almost ideal experimental circumstances for experimental demonstrations of quantum effects. In this device quantum interference between beams spatially separated on a macroscopic scale is put on explicit view. Recently, a new counter-intuitive phenomenon, called quantum Cheshire-cat, is observed in a neutron interferometer experiment. Weak measurement and weak values justify the access of the neutrons’ dynamics in the interferometer. Moreover, another experiment reported full determination of weak-values of neutron’s ½-spin; this experiment is further applied to demonstrate quantum Pigeonhole effect and quantum contextual. In my talk, I am going to give an overview of neutron interferometry for investigation of quantum paradoxes.

We propose and theoretically investigate the implementation of entangling operations on two two-level atoms using cavity-QED scenarios. The atoms interact with an optical cavity and their state is postselected in a noninvasive way by measuring the optical field after the interaction. We show that the resulting quantum operation can be exploited to implement an entanglement purification protocol, where a fidelity larger than one half with respect to any Bell state is not a necessary condition.

Introducing a new field which makes the Hamiltonian unbounded, we show that vacuum fluctuations of a scalar field destabilized the flatspace. Perturbation in this new scalar field, may also explain some astrophysical phenomena in the galactic scale.

In classical mechanics, only the initial state of the system is needed to determine its time evolution. Additional information on the final state is either redundant or inconsistent. In quantum mechanics, however, the initial state does not convey all measurements’ outcomes. Only when augmented with a final quantum state, which can be understood as propagating backwards in time, a richer, more complete picture of quantum reality is portrayed. This time-symmetric view leads to a subtle kind of a local hidden-variables theory, where true collapse never occurs, yet can be effectively observed. Moreover, the Born rule and the borderline between classical and quantum systems can be derived from, respectively, the requirements of stability and “macroscopic robustness under time-reversal.’’ The significant role of macroscopic systems in amplifying and recording quantum outcomes then directly follows. Some possible cosmological consequences of this construction are discussed, especially those related to the breakdown of the “Pigeonhole principle” and our on-going work on the concept of “Quantum Holism”. The talk will be partially based on: 1. Y. Aharonov, E. Cohen, E. Gruss, T. Landsberger, Quantum Stud.: Math. Found. 1 (2014) 133-146. 2. Y. Aharonov, E. Cohen, A.C. Elitzur, Ann. Phys. 355 (2015) 258-268. 3. Y. Aharonov, E. Cohen, to be published in “Quantum Nonlocality and Reality”, M. Bell and S. Gao (Eds.), Cambridge University Press, arXiv:1504.03797. 4. E. Cohen, Y. Aharonov, to be published in “Quantum Structural Studies: Classical Emergence from the Quantum Level”, R.E. Kastner, J. Jeknic-Dugic, G. Jaroszkiewicz (Eds.), World Scientific Publishing Co., arXiv:1602.05083.