Quantum Physics

The field of quantum information provides fundamental insight into central open questions in quantum thermodynamics and quantum many-body physics, such as the characterization of the influence of quantum effects on the flow of energy and information. These insights have inspired new methods for cooling physical systems at the quantum scale using tools from quantum information processing. These protocols not only provide an essentially different way to cool, but also go beyond conventional cooling techniques, bringing important applications for quantum technologies. In this talk, I will first review the basic ideas of algorithmic cooling and give analytical results for the achievable cooling limits for the conventional heat-bath version. Then, I will show how the limits can be circumvented by using quantum correlations. In one algorithm I take advantage of correlations that can be created during the rethermalization step with the heat-bath and in another I use correlations present in the initial state induced by the internal interactions of the system. Finally, I will present a recently fully characterized quantum property of quantum many-body systems, in which entanglement in low-energy eigenstates can obstruct local outgoing energy flows.

Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a space-time structure and forbids signalling outside the future. On the other hand, causality can be defined operationally using causal models by considering the flow of information within a network of physical systems and interventions on them. From both a foundational and practical viewpoint, it is useful to establish the class of causal models that can coexist with relativistic principles such as no superluminal signalling, noting that causation and signalling are not equivalent. We develop such a general framework that allows these different notions of causality to be independently defined and for connections between them to be established. The framework first provides an operational way to model causation in the presence of cyclic, fine-tuned and non-classical causal influences. We then consider how a causal model can be embedded in a space-time structure and propose a mathematical condition (compatibility) for ensuring that the embedded causal model does not allow signalling outside the space-time future. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. We then demonstrate the mathematical possibility of causal loops embedded in Minkowski space-time that can be operationally detected through interventions, without leading to superluminal signalling. Our framework provides conditions for preventing superluminal signalling within arbitrary (possibly cyclic) causal models and also allows us to model causation in post-quantum theories admitting jamming correlations. Applying our framework to such scenarios, we show that post-quantumjamming can indeed lead to superluminal  signalling contrary to previous claims. Finally, this work introduces a new causal modelling concept of ``higher-order affects relations'' and several related technical results, which have applications for causal discovery in fined-tuned causal models.

The Quantum Bayesian, or QBist, interpretation regards the quantum formalism to be a tool that a single agent may adopt to help manage their expectations for the consequences of their actions. In other words, quantum theory is an addition to decision theory, and its shape, we hope, can teach us something about the nature of reality. Beyond simple consistency, an interpretation is judged by its capacity to point the way forward. In the first half of the talk, I will highlight several ways in which my collaborators and I have applied QBist intuitions to pose and solve technical questions regarding the informational structure and conceptual function of quantum theory. At the root of many of these developments is the notion of a reference measurement, the key to a probabilistic representation of quantum theory. In this setting, we can explore the boundary of the quantum reasoning structure from a uniquely QBist angle. Working with such representations grants a new perspective and inspires questions which wouldn't have occurred otherwise; as examples, we will meet downstream results concerning quantum channels, discrete quasiprobability representations, and a variant of the information-disturbance tradeoff. Most recently, I have pursued ways in which QBism could be applied to the construction of new tools and strategies for existing problems in quantum information and computation. In the second half of the talk, we will encounter the first of these, an agent-based modeling proposal where multiple, suitably interacting, QBist decision-makers might collectively work out the solution to a task of interest in the right circumstances. I will describe some initial explorations of modeling agent belief dynamics in two contexts: first, an expectation sampling interaction with an eye to agential agreement, and, second, a setting where agents are players of quantum games. In the future, we imagine it is possible that a sufficiently mature development of the agent-based program we have begun could suggest new approaches to quantum algorithm design.

Zoom Link: https://pitp.zoom.us/j/95668668835?pwd=MUJtRGMxbEFzSEdVVmZ3TkR3dVVVZz09

Aside from quantum mechanics, other areas in physics constrain information processing. From relativity, we know information cannot move faster than the speed of light. In quantum gravity, we expect but don't fully understand additional constraints, for instance on how densely information can be stored. Can we develop an understanding of information processing in the context of quantum gravity? Towards doing so, we consider quantum information within ``holographic'' spacetimes, which have an alternative, non-gravitational, description. In that context questions about information processing in the presence of gravity can be translated to different questions about quantum information without gravity. As a specific example, we study constraints on computation within a gravitating region, and use the holographic description to argue that gravity constrains the complexity of operations that can happen inside the region. Along the way, we are led to new connections relating quantum gravity, position-based cryptography, quantum secret sharing and complexity theory. 

Topological quantum codes illustrate a variety of concepts in quantum many-body physics. They also provide a realistic and resource-efficient approach to building scalable quantum computers. In this talk, I will focus on fault-tolerant quantum computing with a new topological code, the 3D subsystem toric code (STC). The 3D STC can be realized on the cubic lattice by measuring small-weight local parity checks. The 3D STC is capable of handling measurement errors while performing reliable quantum error correction and implementing logical gates in constant time. This dramatically reduces the computational time overhead and gives the 3D STC a resilience to time-correlated noise.

The formalism of quantum theory over discrete systems is extended in two significant ways. First, tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates. Second, quantum evolutions are generalized to act over network configurations, in such a way that nodes be allowed to merge, split and reconnect coherently in a superposition. The hereby presented mathematical framework is anchored on solid grounds through numerous lemmas. Indeed, one might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the partitioning of systems becomes both logical and dynamical. Such interrelations in fact carry through, albeit two new notions become instrumental: consistency and comprehension.

Joint work with Amélia Durbec and Matt Wilson

Reference: https://arxiv.org/abs/2110.10587

Zoom Link: https://pitp.zoom.us/j/97185954578?pwd=OC9mUzl4L3V4WDZzVEZoekpOS24wQT09

The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the often assumed no-restriction hypothesis, the set of accessible measurements within a given theory can be limited for different reasons, and this raises a question of what restrictions on measurements are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of measurements. We distinguish three classes of such operational restrictions: restrictions on measurements originating from restrictions on effects; restrictions on measurements that do not restrict the set of effects in any way; and all other restrictions. As a setting to detect nonclassicality in restricted theories we consider generalizations of random access codes, an intriguing class of communication tasks that reveal an operational and quantitative difference between classical and quantum information processing. We formulate a natural generalization of them, called random access tests, which can be used to examine collective properties of collections of measurements. We show that the violation of a classical bound in a random access test is a signature of either measurement incompatibility or super information storability, and that we can use them to detect differences in different restrictions.
 

This talk consists of two parts. At first, I will focus on geometric obstructions to decoding Hawking radiation (python’s lunch). Harlow and Hayden argued that distilling information out of Hawking radiation is computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. I will trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, I will present a conjecture that relates the computational hardness of distilling information to geometric features of the wormhole.

Then, with the long-term goal of studying quantum gravity in the lab, I will discuss a proposal for a holographic teleportation protocol that can be readily executed in table-top experiments. This protocol exhibits similar behavior to that seen in recent traversable wormhole constructions. I will introduce the concept of "teleportation by size" to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call "size winding". 

Zoom Link: https://pitp.zoom.us/j/93957279481?pwd=eGVTU1MwOGNWNkMyYlRiWGo0QnFldz09

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the logarithmic Sobolev constant, which is equivalent to some form of entropy decay. For classical spin systems, the positivity of such constants follows from a mixing condition on the Gibbs measure, via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the logarithmic Sobolev constant associated to the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. Subsequently, we apply it to show that for a finite-range, translation-invariant commuting Hamiltonian on a spin chain, the Davies semigroup describing the reduced dynamics resulting from the joint Hamiltonian evolution of a spin chain weakly coupled to a large heat bath thermalizes rapidly at any temperature. This, in particular, rigorously establishes the absence of dissipative phase transition for Davies evolutions over translation-invariant spin chains.
 

Bell’s theorem is typically understood as proof that quantum theory is incompatible with local hidden variable (LHV) models. In recent years, however, LHV models have been recognized as a particular and simple case of much more general causal networks that can give rise to new and stronger forms of nonclassicality. And, since nonlocality is a resource in a variety of applications, it is thus natural to ask whether these novel forms of nonclassical behavior can also be put to use in information processing. In this seminar, I will present recent results exploring quantum correlations in several such causal scenarios, ranging from foundational questions such as freedom of choice in Bell experiments to more applied situations covering cryptography, distributed computing, and game theory.

Zoom Link: TBD