Session E58: Quantum Foundations

Cause and Effect in a Quantum World

Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner that Reichenbach's principle would seem to demand. From this perspective, Bell’s theorem is best understood as a challenge to providing a satisfactory causal explanation of the observed statistics (rather than as a challenge to maintaining locality and realism, as it is usually construed). A promising avenue to meet this challenge is to find an intrinsically quantum counterpart to Reichenbach’s principle. We here propose such a generalization and provide it with a rigorous justification that parallels the justification that can be given for the classical version. Specifically, we demonstrate that under the assumption that systems with no causal connection are represented by a product state and that quantum dynamics is fundamentally unitary, if a quantum system A is a complete common cause of quantum systems B and C, then the quantum channel from A to BC factorizes in a particular way. Finally, we show how to generalize our quantum version of Reichenbach's principle to a formalism for quantum causal models, and provide examples of how the formalism works. Joint work with John-Mark A. Allen, Jonathan Barrett, Dominic C. Horsman, and Ciaran M. Lee.   

Finally making sense of the double-slit experiment

Feynman stated that the double-slit experiment “. . . has in it the heart of quantum mechanics. In reality, it contains the only mystery” and that “nobody can give you a deeper explanation of this phenomenon than I have given; that is, [just] a description of it.” We rise to the challenge with an alternative to the wave function-centered interpretations: instead of a quantum wave passing through both slits, we have a localized particle with nonlocal interactions with the other slit [Aharonov, Cohen, Colombo, Landsberger, Sabadini, Struppa & Tollaksen, Proc Natl Acad Sci, vol 114 iss 25 (2017)]. Key to this explanation is dynamical nonlocality, which naturally appears in the Heisenberg picture as nonlocal equations of motion. This insight led us to develop an approach to quantum mechanics which relies on pre- and post-selection, weak measurements, deterministic, and modular variables. This fundamental change in perspective towards a new ontology points to deterministic properties within the Heisenberg picture as being the primitives instead of the wavefunction, which remains an ensemble property. Using this new approach in a double-slit experiment, we can verify that the particle, which is localized, goes through only one of the slits. In addition to this corpuscular behavior, a nonlocal property originating from the other, distant, slit has been affected through the nonlocal Heisenberg equations of motion. Although the Heisenberg and Schroedinger pictures are equivalent formulations, nevertheless, the framework presented here has led to new insights, intuitions, and experiments that were missed from the old perspective. For example, this new perspective affects the axiomatic structure of quantum mechanics: under the assumption of nonlocality, uncertainty turns out to be crucial to preserve causality. Hence, a (qualitative) uncertainty principle can be derived rather than assumed.   

Testing quantum mechanics and gravity with levitated optomechanics

We will report on recent progress in levitated optomechanics experiments in order to test the quantum superposition principle as well as the interplay between quantum mechanics and gravity. The mass of nanoparticles is large compared to the mass of single atoms and experiments manipulating such particles in vacuum are promising to test both theories in a new parameter regime. The mass of these particles is small enough so that the generation of non-classical centre of mass motional states, such as spatial superposition states, is not impossible - but at the same time the mass is large enough so that the effects of gravity become significant for the dynamics of those non-classical states. This represents a new paradigm to test quantum mechanics and gravity in the low energy - non-relativistic regime. We will discuss recent proposals for concrete expriments as well as report on their feasiblty based on experimental state of the art.   

Measuring a deviation from the Superposition Principle in slit based interference experiments: towards a non-zero Sorkin parameter

The superposition principle forms the heart of all modern applications and properties of quantum mechanics such as quantum entanglement and quantum computing. However, its usual application to slit based interference experiments has caveat in both optics and quantum mechanics where it is often incorrectly assumed that the boundary condition represented by slits opened individually is same as them being opened together. In theory work carried out over the last few years, we have quantified the correction term in terms of the Sorkin parameter [1,2]. In this talk, we will report the first reported measurement of a deviation from the superposition principle in the microwave domain using antennas as sources and detectors of the electromagnetic waves. This deviation is quantified through the Sorkin parameter which can be as big as 6% in our experiment [3]. Measuring a non-zero Sorkin parameter not only gives experimental verification to the theoretical predictions about the deviation from the superposition principle in interference experiments, it also exemplifies an experimental scenario in which non zero Sorkin parameter need not necessarily imply falsification of Born rule for probabilities in quantum mechanics which has been the basis for several experiments in recent years [4].

1. R.Sawant, J.Samuel, A.Sinha, S.Sinha, U.Sinha, Non classical paths in quantum interference experiments. Phys.Rev.Lett. 113, 120406, 2014.
2. A.Sinha, Aravind H.V., U.Sinha, On the Superposition principle in interference experiments. Scientific Reports 5, 10304, 2015.
3. G. Rengaraj, Prathwiraj U, Surya Narayana Sahoo, R. Somashekhar and Urbasi Sinha, Measuring the deviation from the superposition principle in interference experiments, arXiv:1610.09143.
4. U.Sinha, C.Couteau, T.Jennewein, R.Laflamme, G.Weihs, Ruling out multi-order interference in quantum mechanics. Science 329, 418-421, 2010.   

Measuring the past of quantum systems: from counting quantum pigeons to watching atoms as they tunnel

In quantum mechanics, as in the classical world, one can draw some conclusions from present observations about the past behaviour of a system. The question of just what one can say about a system given knowledge of its preparation and its final state remains a topic of discussion. I will present a number of recent and ongoing experiments which address these issues by applying weak measurements (in the sense of Aharonov, Albert, and Vaidman) and post-selected strong measurements (\`a la Aharonov, Bergmann, and Lebowitz) to systems ranging from entangled photons to tunneling atoms to quantum-level laser beams interacting through an optical nonlinearity. Such measurements offer insight into processes such as tunneling, but are also well known to lead to some results which violate our intuitive expectations. Applying variable-strength measurements to the ``pigeonhole paradox'' will allow us to probe just how certain aspects of these ``conditional measurements'' remain robust, independent of measurement strength, while other axioms and sum rules behave quite differently in different regimes. I will also discuss how a weak measurement of photon number may exceed the number of prepared photons, and what weak measurements tell us about where particles ``spend their time'' while tunneling through a barrier.