Quantum Foundations

A toy model due to Spekkens is constructed by applying an epistemic restriction to a classical theory but reproduces a host of phenomena that appear in quantum theory. The model advances the position that the quantum state may be interpreted as a reflection of an agent’s knowledge. However, the model fails to capture all quantum phenomena because it is non-contextual. Here we show how a theory similar to the one Spekkens proposes requires only a single augmentation to give quantum theory for certain systems. Specifically, one must combine all possible epistemically restricted classical accounts of a quantum experiment. The rule for combination is simple: sum the nonrandom parts of all classical predictions to arrive at the nonrandom part of the quantum prediction.

It is commonplace that quantum theory can be viewed as a ``non-classical" probability calculus. This observation has inspired the study of more general non-classical probabilistic theories modeled on QM, the so-called generalized probabilistic theories or GPTs. However, the boundary between these putatively non-classical probabilistic theories and classical probability theory is somewhat blurry, and perhaps even conventional. This is because, as is well known, any probabilistic model can be understood in classical terms if we are willing to embrace some form of contextuality. In this talk, I want to stress that this can often be done functorially: given a category $\Cat$ of probabilistic models, there are functors $F : \Cat \rightarrow \Set_{\Delta}$ where $\Set_{\Delta}$ is the category of sets and stochastic maps. In addition to the familiar Beltrametti-Bugajski representation, I'll exhibit two others that are less well known, one involving the ``semi-classical cover" and another, slightly more special, that allows one to represent a probabilistic model with sufficiently strong symmetry properties by a model having a completely classical probabilistic structure, in which any ``non-classicality" is moved into the dynamics, in roughly the spirit of Bohmian mechanics. 

(Based on http://philsci-archive.pitt.edu/16721/)

Zoom Link: https://pitp.zoom.us/j/91838172434?pwd=SUltOGlURWI5MDN6Qk45dnVRelBOQT09

The standard operational probabilistic framework (within which Quantum Theory can be formulated) is time asymmetric.  This is clear because the conditions on allowed operations include a time asymmetric causality condition.  This causality condition enforces that future choices do not influence past events.  To formulate operational theories in a time symmetric way I modify the basic notion of an operation allowing classical incomes as well as classical outcomes.  I provide a new time symmetric causality condition which I call double causality.  I apply these ideas to Quantum Theory proving, along the way, a time symmetric version of the Stinespring extension theorem using double causality.  I also propose the idea of a conditional frame of reference.  We can transform from the time symmetric frame of reference to a forward or a backward frame of reference.  This talk is based on arXiv:2104.00071.

We give a complete characterization of the (non)classicality of all stabilizer subtheories. First, we prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd dimensions, namely Gross’s discrete Wigner function. This representation is equivalent to Spekkens’ epistemically restricted toy theory, which is consequently singled out as the unique noncontextual ontological model for the stabilizer subtheory. Strikingly, the principle of noncontextuality is powerful enough (at least in this setting) to single out one particular classical realist interpretation. Our result explains the practical utility of Gross’s representation, e.g. why (in the setting of the stabilizer subtheory) negativity in this particular representation implies generalized contextuality, and hence sheds light on why negativity of this particular representation is a necessary resource for universal quantum computation in the state injection model. This last fact, together with our result, implies that generalized contextuality is also a necessary resource for universal quantum computation in this model. In all even dimensions, we prove that there does not exist any nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory, and, hence, that the stabilizer subtheory is contextual in all even dimensions.

Ontic structural realism is a form of scientific realism based on quantum mechanics in two ways:
(i) particles are not taken to be individual entities because they are not distinguishable; and, (ii) entanglement is taken to be relational structure that does not reduce to the state of parts and their causal interactions.

Furthermore, the idea of modal structure in OSR is exemplified by the way quantum mechanics sits between Bell-inequality violation and no-superluminal signalling. However, what should the advocate of OSR say about the measurement problem and decoherence? Wallace and Saunders combines OSR with Everettianism and argue that they need each other. Are Ladyman and Ross justified in their reluctance to agree with him?

Classical probabilistic models of quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources for information processing tasks.  A common feature of these models is the presence of inaccessible information, as captured by the concept of preparation contextuality:  There are ensembles of quantum states described by the same density operator, and hence operationally indistinguishable, and yet in any probabilistic (ontological) model, they should be described by distinct probability distributions.  In this talk, I discuss a method for quantifying this inaccessible information and present a family of lower bounds on this quantity in terms of experimentally measurable quantities. These bounds, which can also be interpreted as a new class of robust non-contextuality inequalities, are obtained based on a family of guessing games.  As an application of this result, I derive a noise threshold for the presence of contextually in a noisy system, in terms of the average gate fidelity of the noise channel.

Experimental metaphysics is the study of how empirical results can reveal indisputable facts about the fundamental nature of the world, independent of any theory. It is a field born from Bell’s 1964 theorem, and the experiments it inspired, proving the world cannot be both local and deterministic. However, there is an implicit assumption in Bell’s theorem, that the observed result of any measurement is absolute (it has some value which is not ‘relative to its observer’). This assumption may be called into question when the observer becomes a quantum system (the “Wigner’s Friend” scenario), which has recently been the subject of renewed interest. Here, building on work by Brukner, we derive a theorem, in experimental metaphysics, for this scenario [1]. It is similar to Bell’s 1964 theorem but dispenses with the assumption of determinism. The remaining assumptions, which we collectively call "local friendliness", yield a strictly larger polytope of bipartite correlations than those in Bell's theorem (local determinism), but quantum mechanics still allows correlations outside the local friendliness polytope.  We illustrate this in an experiment in which the friend system is a single photonic qubit [1]. I argue that a truly convincing experiment could be realised if that system were a sufficiently advanced artificial intelligence software running on a very large quantum computer, so that it could be regarded genuinely as a friend. I will briefly discuss the implications of this far-future scenario for various interpretations and modifications of quantum theory.

[1] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde and Howard M. Wiseman, “A strong no-go theorem on the Wigner’s friend paradox", Nature Physics (2020).

The prepare-and-measure scenario is ubiquitous in physics. However, beyond the paradigmatic example of dense coding, there is little known about the correlations p(b|x,y) that can be generated between a sender with input x and a receiver with input y and outcome b. Contrasting dense coding, we show that the most powerful protocols based on qubit communication require high-dimensional entanglement. This motivates us to systematically characterise the sets of correlations achievable with classical and quantum communication, respectively, assisted by a potentially unbounded amount of entanglement. We obtain two different SDP hierarchies for both the classical and quantum case: one based on NPA and one based on informationally-restricted correlations. In the talk, I will discuss the advantages and drawbacks of each, and show that they can be used obtain tight or nearly-tight bounds on in several concrete case studies. As examples of applications, these new tools are used to construct device-independent dimension witnesses robust to unbounded shared entanglement and several resource inequalities for quantum communications.

Agency accounts of causation are often criticised as being unacceptably subjective: if there were no human agents there would be no causal relations, or, at the very least, if humans had been different then so too would causal relations. Here we describe a model of a causal agent that is not human, allowing us to explore the latter claim.   

Our causal agent is special kind of open, dissipative physical system, maintained far from equilibrium by a low entropy source of energy, with accurate sensors and actuators. It has a memory to record sensor measurements and actuator operations, and a learning system that can access the sensor and actuator records to learn and represent the causal relations. We claim that causal relations are relations between the internal sensor and actuator records and the causal concept inherent in these correlations is then inscribed in the physical dynamics of the internal learning machine. We use this model to examine the relationships between three familiar asymmetries aligned with causal asymmetry: time's arrow, the thermodynamic arrow and the arrow of deliberation and action. We consider both classical and quantum agent models and illustrate some differences between the two. 
 

The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios . Most surprisingly, we discover contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations we demonstrate the monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.

With ongoing efforts to observe quantum effects in larger and more complex systems, both for the purposes of quantum computing and fundamental tests of quantum gravity, it becomes important to study the consequences of extending quantum theory to the macroscopic domain. Frauchiger and Renner have shown that quantum theory, when applied to model the memories of reasoning agents, can lead to a conflict with certain principles of logical deduction. Is this incompatibility a peculiar feature of quantum theory, or can modelling reasoning agents using other physical theories also lead to such contradictions? What features of physical theories are responsible for such paradoxes? 

Multi-agent paradoxes have been previously analysed only in quantum theory. To address the above questions, a framework for analysing multi-agent paradoxes in general physical theories is required. Here, we develop such a framework that can in particular be applied to generalized probabilistic theories (GPTs). We apply the framework to model how observers’ memories may evolve in box world, a post-quantum GPT and using this, derive a stronger paradox that does not rely on post-selection. Our results reveal that reversible, unitary evolution of agents’ memories is not necessary for deriving multi-agent logical paradoxes, and suggest that certain forms of contextuality might be. 

https://iopscience.iop.org/article/10.1088/1367-2630/ab4fc4

A series of recent works has shown that placing communication channels in a coherent superposition of alternative configurations can boost their ability to transmit information. Instances of this phenomenon are the advantages arising from the use of communication devices in a superposition of alternative causal orders, and those arising from the transmission of information along a superposition of alternative trajectories. The relation among these advantages has been the subject of recent debate, with some authors claiming that the advantages of the superposition of orders could be reproduced, and even surpassed, by other forms of superpositions. To shed light on this debate, we develop a general framework of resource theories of communication. In this framework, the resources are communication devices, and the allowed operations are (a) the placement of communication devices between the communicating parties, and (b) the connection of communication devices with local devices in the parties' laboratories. The allowed operations are required to satisfy the minimal condition that they do not enable communication independently of the devices representing the initial resources. The resource-theoretic analysis reveals that the aforementioned criticisms on the superposition of causal orders were based on an uneven comparison between different types of quantum superpositions, exhibiting different operational features.

Ref. https://iopscience.iop.org/article/10.1088/1367-2630/ab8ef7