Session M38: Focus Session: Quantum Foundations and Technologies II

Contextuality: a benchmark for ``quantumness'' in theory and experiment

An ontological model for a quantum experiment is a purported explanation for the probabilities we see. Non-contextual models are particularly compelling because they never offer two different explanations for the same observations. I will review these notions and argue that the impossibility of non-contextual models is a good way to rigorously define ``genuine quantumness''. Two examples of phenomena whose ``quantumness'' have been debated are ``anomalous weak values'' and ``logical pre- and post-selection paradoxes''. I will outline how their incompatibility with non-contextual models clarifies why both defy compelling classical explanation. A related idea is to use contextuality to certify that an experiment has achieved quantum coherence without requiring a full characterization. To this end I will present a simple yet robust non-contextuality inequality that can be violated with a single qubit. (The work on pre- and post-selection paradoxes was done in collaboration with with Matt Leifer.)   

Ordering relations for quantum states

It is often desirable to model physical states in an order-theoretic manner, e.g. as a partially ordered set. Classical states are known to possess a unique ordering relation corresponding to a neo-realist interpretation of these states. No such unique relation exists for quantum states. This lack of a unique ordering relation for quantum states turns out to be a manifestation of quantum contextuality vis-\`{a}-vis the Kochen-Specker theorem. It also turns out that this provides a link to certain large-scale thermodynamic processes. The suggestion that the ordering of quantum states leads to macroscopic thermodynamic processes is at least five decades old. The suggestion that the mechanism that drives the ordering is contextuality, is unique to this work. The argument is framed in the language of the theories of domains, categories, and topoi.   

Advances in weak-values based metrology

We theoretically [1] and experimentally [2] describe the relative advantages of implementing weak-values-based metrology versus standard methods. To accomplish this, we measure small optical beam deflections both a weak-values-based technique, and a standard technique. By introducing controlled external modulations of the detector, and transverse beam-jitter, we quantify the mitigation of these sources in the weak values-based experiment versus the standard experiment. In all cases, the weak-values technique performs the same or better than the standard technique by up to two orders of magnitude in precision for our parameters. We further measure the statistical efficiency of the weak-values-based technique. By post-selecting on 1\% of the photons, we obtain 99\% of the available Fisher information of the beam deflection parameter. We also discuss ways to recycle the discarded events [3], obtaining much greater precision on a measured parameter.\\[4pt] [1] A. N. Jordan, J. Mart\'inez-Rinc\'on, J. C. Howell, Phys. Rev. X 4, 011031 (2014).\\[0pt] [2] G. I. Viza, J. Mart\'inez-Rinc\'on, G. B. Alves, A. N. Jordan, J. C. Howell, arXiv:1410.8461 (2014).\\[0pt] [3] J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).   

On the efficacy of weak measurements for tomography

Recently there has been a fascination with weak measurements in the field of tomography. We conduct a detailed analysis of two specific schemes: so-called ``direct state tomography'' and another scheme marketed as outperforming ``standard'' tomography with respect to fidelity considerations. Through the application of generalized measurement theory we clearly identify what weak measurements contribute beyond ``standard'' projective measurements and what simple techniques the application of weak measurements obscures.   

Many Worlds, the Born Rule, and Self-Locating Uncertainty

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born Rule: why is the probability given by the square of the amplitude? Recently, Page has raised another puzzle: the Born Rule itself is insufficient in cases where the wave function includes multiple indistinguishable observers in the same branch. I will argue that both problems share a common solution, arising from a proper treatment of self-locating uncertainty (physical situations containing multiple copies of identical observers). This analysis gives a simple, physics-oriented derivation of the Born Rule, as well as a justification for the treatment of identical classical observers.   

Quantum phenomena modelled by interactions between many classical worlds

[Ref: Phys. Rev. X 4 041013 (2014).] We investigate how quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but countable, number of classical ``worlds,'' and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here a ``world'' means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach each world evolves deterministically; probabilities arise due to ignorance as to which world a given observer occupies; and we argue that in the limit of infinitely many worlds the wave function can be recovered (as a secondary object) from the motion of these worlds. We introduce a simple model of such a ``many interacting worlds'' approach and show that it can reproduce some generic quantum phenomena--such as Ehrenfest's theorem, wavepacket spreading, barrier tunneling and zero point energy--as a direct consequence of mutual repulsion between worlds. Finally, we perform numerical simulations using our approach. We demonstrate, first, that it can be used to calculate quantum ground states, and second, that it is capable of reproducing, at least qualitatively, the double-slit interference phenomenon.   

Does protective measurement imply the reality of the quantum state?

In 1993, Aharonov and Vaidman claimed that the quantum state of a single system could be measured in a scheme they called ``protective measurement'' and hence that the quantum state must be a real property of a single system. Despite attracting considerable controversy, we do not think that the existing criticisms have put their finger on precisely what is wrong with this claim. We explain why we think that, in the protective measurement scheme, the vast majority of the information about the quantum state comes from the protection operation rather than from the state itself. We also give simple toy models of protective measurement which show that the protection operation effectively reprepares the system in an independent copy of the initial state. Thus determining the quantum state by protective measurement is conceptually no different from performing state tomography on an ensemble of independently prepared systems.   

Most likely paths for quantum trajectories: multiple solutions and generalization to two-qubit case

We study trajectories of quantum states evolving under the quantum measurement. We further analyze and develop our recent approach for finding the most likely path for quantum trajectories between any two states at two different times. Under certain conditions, we find that the most likely path can bifurcate and multiple solutions do exist. Two or more solutions can have comparably large probability weights associated with them, implying multiple likely paths for the state trajectories. In developing the approach, we go beyond a single system and apply the theory to a system with two qubits. We find paths that are most likely taken between separable states and entangled states. We, furthermore, present the theoretical findings along with a preliminary comparison to data from the experiment of superconducting transmon qubits coupled to microwave cavities.\\[4pt] [1] A. Chantasri, J. Dressel, A. N. Jordan, Phys. Rev. A 88, 042110 (2013)\\[0pt] [2] S. J. Weber, A. Chantasri, J. Dressel, A. N. Jordan, K. W. Murch, I. Siddiqi, Nature 511, 570-573 (2014)   

Microscopic derivation of open quantum Brownian motion

Recently a model of open quantum Brownian motion (OQBM) [M. Bauer, D. Bernard, A. Tilloy, Phys. Rev. A 88 (2013) 062340] was introduced as a scaling limit of Open Quantum Walks (OQWs) [S. Attal, F. Petruccione, C. Sabot, I. Sinayskiy, J. Stat. Phys. 147 (20120 832]. OQBM is a new type of quantum Brownian motion where the dynamics of the Brownian particle not only depends on the interactions with a thermal environment, but also depends on the state of the internal degrees of freedom of the Brownian particle. Here, we present the microscopic derivation of the OQBM for a Brownian particle with two internal degrees of freedom. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented.   

Entanglement-assisted weak measurement

Postselected weak measurement with a large measurement can amplify small coupling parameters. However, a major shortcoming is that the postselection probability is usually very low when the amplification is large, which means an enormous amount of resources is necessary. So, how to increase the postselection probability is an important problem in practical application of weak measurement. In this work, we study the optimization of weak measurement and propose an entanglement-assisted protocol for it. We start from maximizing the postselection probability with a given weak value. The result shows the maximum postselection probability is proportional to the variance of the observable under the initial state of the system. As is know that the variance has different scaling under entangled or uncorrelated states, it inspired us to show using entanglement in the initial state of the system can increase the postselection efficiency beyond that with sequential use of systems. With this result, we further find the Fisher information of weak measurement can approximately reach the Heisenberg limit with the assistance of entanglement. Finally, we give simple quantum circuits for the implementation of this protocol with qubits, including initialization, weak interaction and postselection.   

Pricing postselection: the cost of indecision in state discrimination

Postselection is the process of discarding outcomes from statistical trials that are not the event one desires. Postselection can be useful in many applications where the cost of getting the wrong event is implicitly high. However, unless this cost is specified exactly, one might formally conclude that discarding all data is optimal. Here we analyze the optimal decision rules and quantum measurements in a decision theoretic setting where a pre-specified cost is assigned to discarding data. Non-trivial solutions are found for even the simplest state discrimination problem of choosing between two nonorthogonal qubit states. Our solutions interpolate between the Helstrom measurement and the unambiguous state discrimination experiment.