Quantum Foundations

Quantum mechanics can be seen as a set of instructions how to calculate probabilities by associating mathematical objects to physical procedures, like preparation, manipulation, and measurement of a system. Quantum theory then yields probabilities which are neutral with respect to its use, e.g., in a Bayesian or a frequentistic way. We investigate a different approach to quantum theory and physical theories in general, in which we aim for subjective predictions in the Bayesian sense. This gives a structure different from the operational framework of general probabilistic theories. We explore these differences and the according mathematical language of such probabilistic Bayesian theories. This is joint work with Adan Cabello, Giulio Chiribela, and Markus Müller.

Seven years ago, the first paper was published [1] on what has come to be known as the “Many Interacting Worlds” (MIW) interpretation of quantum mechanics (QM) [2,3,4]. MIW is based on a new formulation of QM [1,5,6], in which the wavefunction Ψ(t, x) is discarded entirely. Instead, the quantum state is represented as an ensemble, x(t, C), of quantum trajectories or “worlds.” Each of these worlds has well-defined real-valued particle positions and momenta, and is thereby classical-like. Unlike a classical ensemble, however, nearby trajectories/worlds can interact with each other dynamically, giving rise to quantum effects. In this respect, MIW is very different from the Everett Many-Worlds Interpretation (MWI); another key difference is that no world branching occurs.

The MIW approach offers a direct “realist” description of nature that may be beneficial in interpreting quantum phenomena such as entanglement, measurement, spontaneous decay, etc. It provides a useful analysis of MWI, explaining how the illusion of world branching emerges in that context. Moreover, x(t, C) satisfies a trajectory-based action principle, which allows quantum theory (via the Euler-Lagrange equation and Noether’s theorem) to be placed on the same footing as classical theories. In this manner, a straightforward relativistic generalization can also be obtained [7,8], which offers a notion of global simultaneity even for accelerating observers. Whereas the original MIW theory is fully consistent with Schroedinger wave mechanics, the more recently developed flavors offer the promise of new experimental predictions. These and other developments, e.g. for many dimensions, multiple particles, and spin, may also be discussed.

[1] B. Poirier, Chem. Phys. 370, 4 (2010).
[2] M. J. W. Hall, D.-A. Deckert, and H. Wiseman, Phys. Rev. X 4, 041013 (2014)
[3] B. Poirier, Phys. Rev. X, 4, 040002 (2014).
[4] C. T. Sebens, Phil. Sci. 82, 266 (2015).
[5] P. Holland, Ann. Phys. 315, 505 (2005).
[6] J. Schiff and B. Poirier, J. Chem. Phys. 136, 031102 (2012).
[7] B. Poirier, arXiv:1208.6260 [quant-ph], (2012).
[8] H.-M. Tsai and B. Poirier, EmQM15: Emergent Quantum Mechanics 2015, ed. G. Grössing, (J. Physics, IOP, 2016) 701, 012013.

The path integral formulation of quantum mechanics has been immensely influential, particularly in high energy physics. However, its applications to quantum circuits has so far been more limited. In this talk I will discuss the sum-over-paths approach to computing transition amplitudes in Clifford circuits. In such a formulation, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action which is provided by the discrete Wigner representation. As an application of the sum-over-paths technique I will show how to recover a version of the Gottesman-Knill theorem, namely that the transition amplitudes in Clifford circuits can be computed efficiently.

Device-independent self-testing allows user to identify the measured quantum states and the measurements made in a device using the observed statistics. Such verification scheme only requires assuming the validity of quantum theory and no-signalling. As such, no assumptions are required about the inner-workings of the device. Hence, self-testing allows laymen to test the serviceability of a quantum device without needing its blueprint. This talk will be primarily focused on the self-testing of bipartite entangled pure states [Nat. Comms. 8, 15485 (2017)]. Also, I will be touching on the recent study of the geometry of the quantum set [In preparation].

What can machine learning teach us about quantum mechanics? I will begin with a brief overview of attempts to bring together the two fields, and the insights this may yield. I will then focus on one particular framework, Projective Simulation, which describes physics-based agents that are capable of learning by themselves. These agents can serve as toy models for studying a wide variety of phenomena, as I will illustrate with examples from quantum experiments and biology.

We construct a hidden variable model for the EPR correlations using a Restricted Boltzmann Machine. The model reproduces the expected correlations and thus violates the Bell inequality, as required by Bell's theorem. Unlike most hidden-variable models, this model does not violate the locality assumption in Bell's argument. Rather, it violates measurement independence, albeit in a decidedly non-conspiratorial way.