Quantum Physics

The methodology employed in reconstructing quantum theory involves defining a general mathematical framework that frames a landscape of possible theories and then positing principles that uniquely pick out quantum theory. In contrast, many traditional interpretations of quantum theory consider only quantum theory, not a larger space of possible theories. I will defend the modal methodology used in reconstruction by tracing the historical roots of Einstein’s distinction between principle and constructive theories. Einstein’s principle theories (exemplified by thermodynamics and special relativity) are often cited as inspiration for reconstructing quantum theory. The concept of a “physics of principles” emerged at the end of the nineteenth century in the context of the application of Lagrangian mechanics to electromagnetism. This case is an intriguing historical precedent for reconstructing quantum theory. I will also offer some reflections on how the application of a similar modal methodology in axiomatic QFT plays out. 

Hidden-variables theories account for quantum mechanics in terms of a particular 'equilibrium' distribution of underlying parameters corresponding to the Born rule. In the most well-studied example, the pilot-wave theory of de Broglie and Bohm, it is well established that the Born rule may be understood to arise from a process of dynamical relaxation. This 'quantum relaxation' may have taken place in the very early universe and could have left imprints on the cosmic microwave background (CMB). Such imprints amount to signatures of the decay of early violations of the Born rule. In this colloquium we summarise recent progress in making detailed predictions and in comparing them with the reported large-scale anomalies in the CMB data.

Hidden-variables theories account for quantum mechanics in terms of a particular 'equilibrium' distribution of underlying parameters corresponding to the Born rule. A natural question to ask is whether the theory is stable under small perturbations away from equilibrium. We compare and contrast two examples: de Broglie's 1927 pilot-wave theory and Bohm's 1952 reformulation thereof. It is well established that in de Broglie's dynamics initial deviations from equilibrium will relax. We show that this is not the case for Bohm's dynamics: initial deviations from equilibrium do not relax and in fact grow with time. On this basis we argue that Bohm's dynamics is untenable as a physical theory (while de Broglie's dynamics remains a viable candidate). We advocate stability as a general selection criterion for hidden-variables theories.

In this talk I show how to systematically classify all possible alternatives to the measurement postulates of quantum theory. All alternative measurement postulates are in correspondence with a representation of the unitary group. I will discuss composite systems in these alternative theories and show that they violate two operational properties: purification and local tomography. This shows that one can derive the measurement postulates of quantum theory from either of these properties. I will discuss the relevance of this result to the field of general probabilistic theories. In a second part of the talk I will discuss work in progress and directions for future research. I will show how to generalise the framework used to theories which have different pure states and dynamics than quantum theory. I will discuss two types of theories which can be studied in this framework: Grassmannian theories (same dynamical group and different pure states to quantum theory) and non-linear modifications to the Schrodinger equation (same pure states and different dynamical group).

Science is like puzzle-solving. Making sense of quantum theory is a particularly thorny kind of brain-twister, with more than its fair share of mysteries. If you are stuck on a puzzle, it may be because you have made a false assumption about the nature of some entity that is absolutely central to the whole business. If so, you have made a category mistake: you are not just wrong about what this entity is, but about what sort of thing it is.

In his Public Lecture at Perimeter Institute, Robert Spekkens will explain why he believes that many quantum mysteries are a result of a category mistake concerning the nature of quantum states. Along the way, he will address some idiosyncratic questions, such as: What did Plato have to say about Heisenberg’s uncertainty principle? What do poorly implemented clinical drug trials have to do with "spooky action at a distance"? And, most importantly, what did the successful deciphering of Egyptian hieroglyphs teach us about the interpretation of quantum theory? 

Spekkens is a faculty member at Perimeter Institute whose research examines the foundations of quantum theory. He co-edited the book Quantum Theory: Informational Foundations and Foils, and he is a Project Leader of the international research collaboration "Quantum Causal Structures.” In 2012, he won first prize in the Foundational Questions Institute (FQXi) essay contest "Questioning the Foundations: Which of Our Assumptions Are Wrong?" He lives in Waterloo with his wife and three-year-old son.

Stabilizer states are a rich class of quantum states which can be efficiently classically represented and manipulated. In this talk I will describe some ways in which they can help us to represent and manipulate more general quantum states. I will discuss classical simulation algorithms for quantum circuits which are based on expressing a quantum state as a superposition of (as few as possible) stabilizer states.

Based on arXiv:1601.07601 (with Sergey Bravyi) and work in progress with Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell and Mark Howard.

In this talk I will discuss recently-identified classes of quantum correlations that go beyond nonlocal classical hidden-variable models equipped with communication. First, in the bipartite scenario, I will focus on so-called instrumental causal networks, which are a primal tool in causal inference. There, I will show that it is possible to “fake” classical causal influences with quantum common causes, in a formal sense quantified by the average causal effect (ACE). Furthermore, I will show that it is possible to violate instrumental inequalities with quantum resources, both in the device-independent and in the 1-sided device-independent settings. Second, in the multipartite setting, I will present a causal hierarchy of multipartite nonlocality. I will make special emphasis on quantum correlations in the upper classes of the hierarchy that define stronger forms of genuinely multipartite quantum non-locality than those previously known. The seminar will touch upon concepts like Bell nonlocality and quantum steering as well as Bayesian nets and causal inference.

Adiabatic quantum computation (AQC) is a method for performing universal quantum computation in the ground state of a slowly evolving local Hamiltonian, and in an ideal setting AQC is known to capture all of the computational power of the  quantum circuit model.  However, despite having an inherent robustness to noise as a result of the adiabatic theorem and the spectral gap of the Hamiltonian, it has been a longstanding theoretical challenge to show that fault-tolerant AQC can in principle be performed below some fixed noise threshold.  There are many aspects to this challenge, including the difficulty of adapting known ideas from circuit model fault-tolerance as well as the need to develop an error model that is appropriately tailored for open system AQC.  In this talk I will introduce a scheme for combining Feynman-Kitaev history state Hamiltonians with topological quantum error correction, in order to show that universal quantum computation can be encoded not only in the ground state but also in the finite temperature Gibbs state of a local Hamiltonian.  Using only local interactions with bounded strength and a polynomial overhead in the number of qubits, the scheme is intended to serve as a proof of principle that universal AQC can be performed at non-zero temperature, and also to further our understanding of the complexity of highly entangled quantum systems in thermal equilibrium.

The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This work investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels, by employing tools from random matrix theory, representation theory, combinatorics, Weingarten calculus etc. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Renyi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Renyi entanglement entropies, and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Renyi entanglement entropies to the complexity beyond scrambling/thermalization/chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.  (Refs: 1703.08104, 1709.04313)

(1) Entanglement-enhanced quantum sensing: parameter estimation and hypothesis testing.
(2) Security from entanglement: quantum key distribution.
(3) Entanglement enhanced communication: channel capacity and additivity issues.
(4) Some open problems.

We discuss some applications of a result on the convex combination of the quantum states (that we refer to as convex-split technique) and its variants. In the framework of Quantum Resource theory, we provide an operational way of characterizing the amount of resource in a given quantum state, for a large class of resource theories. Our results use the convex-split technique in the achievability proof, with a matching converse in the one-shot setting.  Building upon the ideas involved in this achievability proof, we show how the technique (and its close counterpart of position-based decoding) can lead to a large family of entanglement-assisted protocols for quantum communication. We sketch close connections between these protocols and the port-based teleportation scheme of Ishizaka and Hiroshima [Phys. Rev. Lett. 101, 240501]. We exploit these connections to obtain a new protocol for entanglement assisted point to point quantum channel coding in the asymptotic and i.i.d. setting, with the rate of entanglement cost and achievable communication matching that of Bennett et. al. [IEEE Trans. Inf. Theory, 48, 2002].  Based on the works arXiv:1410.3031,  arXiv:1708.00381,   arXiv:1702.01940.