Session X33: Quantum Foundations II

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Distinguishability is central to the foundations and applications of quantum information processing. An important task is to understand when quantum measurements are advantageous over their classical counterparts. We consider maximum confidence measurements, which include minimum-error and unambiguous state discrimination as special cases, in a semi-device-independent scenario, for which the state preparation is trusted but not the measurement. We show that maximum confidence measurements are certifiable and that the certified confidence can be greater in quantum theory than in noncontextual theories. A maximum confidence measurement for two states with inconclusive events, the most common experimental scenario, is analysed in detail. Our results relate contextual advantages of quantum distinguishability to the necessary assumptions behind them and may be used to devise quantum information protocols beyond the limitations of noncontextual theories.   

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In 1981, Mermin published a paper in American Journal of Physics that Feynman called, “One of the most beautiful papers in physics that I know.” Therein, Mermin explained the mystery of quantum entanglement per the Bell spin states to the “general reader” without recourse to the formalism of quantum mechanics. He then challenged the “physicist reader” to resolve the mystery in equally accessible terms. In this talk, I will show how the relativity principle, i.e., “no preferred reference frame” (NPRF), answers Mermin’s challenge. Accordingly, NPRF with the fundamental constants c and h, renders special relativity (SR) and non-relativistic quantum mechanics (QM) mutually coherent and comprehensive, contrary to what some believe. Essentially, NPRF applied to the speed of light c leads to the counterintuitive aspects (“mysteries”) of time dilation and length contraction for SR, and NPRF applied to Planck’s constant h leads to the “mysteries” of Bell state entanglement and the Tsirelson bound for QM. Thus, we see an underlying coherence and integrity between SR and QM via its “mysteries” stemming from the relativity principle.   

Live

In light of Bell's theorem, it has been suggested that one way of maintaining locality is to violate the measurement independence assumption, i.e. to allow the hidden variables to depend on the choice of measurement settings. This is variously viewed as retrocausality, superdeterminism, or a violation of free choice. However, when we drop measurement independence, it is not clear that the other assumption of Bell's theorem - local causality - still captures the intended sense of locality. I will argue that it does not and that, in this context, it needs to be upgraded to a stronger assumption called Λ-mediation. I derive how probabilities should decompose in a model that satisfies Λ-mediation, but not measurement independence, and show that such models can reproduce the correlations in a Bell experiment. The Λ-mediation assumption can be generalized to arbitrary causal structures, and the corresponding decomposition of probabilities can be derived, leading to a graphical model that has some similarities to Markov Networks and Factor Graphs.   

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Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the post-quantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. The seminal Agreement Theorem by Aumann (Annals of Statistics, 1976) states that two (classical) agents cannot agree to disagree. We examine the extension of this theorem to no-signalling settings. In particular, we establish an Agreement Theorem for quantum agents. We also construct examples of (post-quantum) no-signalling boxes where agents can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.   

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The notorious Wigner's friend thought experiment has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In this work we formulate a no-go theorem for the persistent reality of Wigner's friend's perception, which allows us to conclude that the perceptions that the friend has of her own measurement outcomes at different times cannot "share the same reality", if seemingly natural quantum mechanical assumptions are met. We show that there is no joint probability distribution for the friend's perceived measurement outcomes at two different times, that depends linearly on the initial state of the measured system and whose marginals reproduce the predictions of unitary quantum theory. This theorem entails that one must either (1) propose a nonlinear modification of the Born rule for two-time predictions, (2) sometimes prohibit the use of present information to predict the future --thereby reducing the predictive power of quantum theory-- or (3) deny that unitary quantum mechanics makes valid single-time predictions for all observers. We briefly discuss which of the theorem's assumptions are more likely to be dropped within various popular interpretations of quantum mechanics.   

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Geometric Quantum Mechanics (GQM) is an approach to quantum mechanics which focuses on the geometric aspects of the manifold of states, rather than on the vector properties of the Hilbert space. I will discuss how GQM inspires a novel set of tools and results to study the phenomenology of quantum systems and their information-theoretic aspects. Particular attention will be devoted to discuss (1) a new notion of statistical state of a quantum system (2) a novel approach to the thermodynamics of quantum systems and (3) a new notion of quantum entropy.

F. Anza, J. P. Crutchfield - Beyond density matrices: Geometric quantum states
https://arxiv.org/abs/2008.08682
F. Anza, J. P. Crutchfield - Geometric Quantum Thermodynamics
https://arxiv.org/abs/2008.08683
F. Anza, J. P. Crutchfield - Geometric Quantum State Estimation
https://arxiv.org/abs/2008.08679   

Live

In the framework of ontological models, the features of quantum
mechanics that emerge as inherently nonclassical always involve properties that
are fine tuned, i.e. properties that hold at the operational level but break at the
ontological level (they only hold for fine tuned values of the ontic parameters).
Famous examples of such features are contextuality and nonlocality. We here
develop a precise theory-independent mathematical framework for characterizing
operational fine tunings. These are distinct from causal fine tunings - already
introduced by Wood and Spekkens in [NJP,17 033002(2015)] - as they do not
involve any assumption on the underlying causal structure. We show how all the
already known examples of operational fine tunings fit into our framework, we
discuss possibly new fine tunings and we use the framework to shed new light on
the relation between nonlocality and generalized contextuality, where the former
can involve a causal fine tuning too, unlike the latter. The framework is also
formulated in the language of category theory and functors.   

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Axiomatic information thermodynamics (Entropy 2018, 20(4), 237) is a formal mathematical system that describes thermodynamic processes including those in which information is acquired, transformed or discarded. A central concept in the theory is the "eidostate", which is a simple array of possible states, including both thermodynamic macrostates and information records. Well-motivated axioms lead to an entropy function that describes the irreversibility of eidostate processes, and this function in turn leads to a unique probability measure for the states and records in a uniform eidostate. Does this development shed light on the kinds of reasoning available to physical agents that observe and intervene in the quantum world?   

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Kirkwood discovered in 1933, and Dirac discovered in 1945, a representation of quantum states that has undergone a renaissance recently. The Kirkwood-Dirac (KD) distribution has been employed to study nonclassicality across quantum physics, from metrology to chaos to the foundations of quantum theory. The KD distribution is a quasiprobability distribution, a quantum generalization of a probability distribution, which can behave nonclassically by having negative or nonreal elements. Negative KD elements signify quantum information scrambling and potential metrological quantum advantages. Nonreal elements encode measurement disturbance and thermodynamic nonclassicality. KD distributions' nonclassicality has been believed to follow necessarily from noncommutation of operators. We show that noncommutation does not suffice. We prove sufficient conditions for the KD distribution to be nonclassical (equivalently, necessary conditions for it to be classical). We also quantify the KD nonclassicality achievable under various conditions. This work resolves long-standing questions about nonclassicality and may be used to engineer quantum advantages.

D. R. M. Arvidsson-Shukur, J. Chevalier Drori, and N. Yunger Halpern, arXiv preprint: arXiv:2009.04468 (2020)   

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The paradigm of multiple interacting agents who each utilize quantum mechanics is central to much of the recent activity in quantum foundations and quantum information. Relevant work in the latter broadly seeks to identify what advantages quantum theory affords us in the multi-agent setting, but, as recent foundational work highlights, there remains confusion over how to appropriately work in such a setting so as to avoid inconsistencies. A careful and consistent treatment of multiple users of quantum theory would allow us to properly interpret extant work and may suggest new approaches in other areas such as algorithm design. The natural starting point for an agent-based treatment is given by the Quantum Bayesian (QBist) approach. Adopting this, we outline a general approach to modeling rational decision making agents who adopt a normative constraint on expectations for the consequences of hypothetical actions. Agents who universally adopt quantum or classical mechanics in all of their reasoning are seen to be special cases of this approach. As an illustration, we consider quantum and classical agents in two physical scenarios: agents receiving data from an exogenous, non-agential, source and two or more agents interacting with each other.   

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We show that one may interpret physical reality as random fields in space-time. These have a probability given by the expectation of a coherent state projection operator, called the Q-function. The resulting dynamical evolution includes retrocausal effects. This suggests that a physical universe exists without requiring observers, but with a well-defined probability for its field configuration. By including the meter dynamics, we show that field trajectories have quantum measurement properties without wave-function collapse, including sharp measured
eigenvalues. We treat continuous and discrete measurements, and show that this model predicts Bell inequality violations for measurements on correlated spins. A discussion is give of a number of well-known quantum paradoxes, showing how these can be treated in a realistic model of measurement. Our theory resolves a number of practical and philosophical issues in quantum measurement, and we compare it with earlier theories.   

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It has been shown that quantum walks on a lattice can give rise to relativistic wave equations like the Dirac equation in the long wavelength limit. To go to multiple particles and describe a quantum field theory in discrete spacetime, a quantum cellular automaton (QCA) is a natural choice. But can a QCA, with purely local dynamics, give rise to a fermionic field theory at long wavelengths? A straightforward QCA construction can work in one spatial dimension, but we prove that this same approach cannot succeed in two or three dimensions. To evade this no-go result, we construct a QCA in a different way, confining distinguishable particles in a totally antisymmetrized subspace, and show that this recovers Dirac field theory at long wavelengths. We show that an analogous construction for bosons can produce Maxwell's theory, and discuss the issues in going from free to interacting fields.   

Live

The PBR-theorem aimed at proving that the wave-function has to represent objective features of a single physical system. There have been many attempts to interpret the wave-function as not representing the objective physical state of a quantum system by abandoning one of the two explicit assumptions of the PBR-theorem: (i) the existence of objective physical states and (ii) preparation independence. I argue that each theory that violates either of these assumptions meets unsurmountable problems. Although these alternative theories are physically possible, they are for several reasons implausible and problematic. I therefore advocate to search for quantum theories that fulfill the assumptions of the PBR-theorem.