Quantum Physics

Quantum computers have emerged as the natural architecture to study the physics of strongly correlated many-body quantum systems, thus providing a major new impetus to the field of many-body quantum physics. While the method of choice for simulating classical many-body systems has long since been the ubiquitous Monte Carlo method, the formulation of a generalization of this method to the quantum regime has been impeded by the fundamental peculiarities of quantum mechanics, including, interference effects and the no-cloning theorem. We overcome those difficulties by constructing a quantum algorithm to sample from the Gibbs distribution of a quantum Hamiltonian at arbitrary temperatures, both for bosonic and fermionic systems. This is a further step in validating the quantum computer as a full quantum simulator, with a wealth of possible applications to quantum chemistry, condensed matter physics and high energy physics.

Even though the security of quantum key distribution has been rigorously proven, most practical schemes can be attacked and broken. These attacks make use of imperfections of the physical devices used for their implementation. Since current security proofs assume that the physical devices' exact and complete specification is known, they do not hold for this scenario. The goal of device-independent quantum key distribution is to show security without making any assumptions about the internal working of the devices. In this talk, I will first explain the assumptions 'traditional' security proofs make and why they are problematic. Then, I will discuss how the violation of Bell inequalities can be used to show security even when a large part of the physical devices is untrusted.

A system of spins with complicated interactions between them can have many possible configurations. Many configurations will be local minima of the energy, and to get from one local minimum to another requires changing the state of very many spins. A system like this is called a spin glass, and at low temperatures tends to get caught for very long times at a local minimum of energy, rather than reaching its true ground state. Indeed, in many cases, finding the ground state energy of a spin glass is a computationally hard problem, too hard to be solved on a classical computer or even a quantum computer in any reasonable amount of time. Which types of interactions give us computationally hard problems and spin glasses? I will survey what is known as we close in on finding the simplest complex spin systems.

Landauer's erasure principle states that there is an inherent work cost associated with all irreversible operations, like the erasure of the data stored in a system. The necessary work is determined by our uncertainty: the more we know about the system, the less it costs to erase it. Here, we analyse erasure in a general setting where our information about that system can be quantum mechanical. In this scenario, our uncertainty, measured by a conditional entropy, may become negative. We establish a general relation between quantum conditional entropies and a physical quantity, the work cost of erasure. As a consequence, we obtain a thermodynamic interpretation of negative entropies: they quantify the work that can be gained by a quantum observer erasing a system. (arXiv: 1009.1630)

We introduce a family of variational ansatz states for chains of anyons which optimally exploits the structure of the anyonic Hilbert space. This ansatz is the natural analog of the multi-scale entanglement renormalization ansatz for spin chains. In particular, it has the same interpretation as a coarse-graining procedure and is expected to accurately describe critical systems with algebraically decaying correlations. We numerically investigate the validity of this ansatz using the anyonic golden chain and its relatives as a testbed. This demonstrates the power of entanglement renormalization in a setting with non-abelian exchange statistics, extending previous work on qudits, bosons and fermions in two dimensions. This is joint work with Ersen Bilgin.

I revisit an example of stronger-than-quantum correlations that was discovered by Ernst Specker in 1960. The example was introduced as a parable wherein an over-protective seer sets a simple prediction task to his daughter's suitors. The challenge cannot be met because the seer asks the suitors for a noncontextual assignment of values but measures a system for which the statistics are inconsistent with such an assignment. I will show how by generalizing these sorts of correlations, one is led naturally to some well-known proofs of nonlocality and contextuality, and to some new ones. Specker's parable involves a kind of complementarity that does not arise in quantum theory - three measurements that can be implemented jointly pairwise but not triplewise -- and therefore prompts the question of what sorts of foundational principles might rule out this kind of complementarity. This is joint work with Howard Wiseman and Yeong-Cherng Liang.

In this talk we quickly review the basics of the modal "toy model" of quantum theory described by Schumacher in his September 22 colloquium at PI. We then consider how the theory addresses more general open systems. Because the modal theory has a more primitive mathematical structure than actual quantum mechanics, it lacks density operators, positive operator measurements, and completely positive maps. As we will show, however, modal quantum theory has an elegant description of the states, effects and operations of open modal systems -- a description with close analogies to actual quantum mechanics.

The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the very inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on an analysis of what it may mean for one tensor to depend in the proper way on another, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime.

Over the last twenty years, quantum information and quantum computing have profoundly shaped our thinking about the basic concepts of quantum physics. But can these insights also shape the way we /teach/ quantum mechanics to undergraduate physics students? A recent adventure in textbook-writing suggests some strategies and dilemmas.

The uncertainty principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, it is possible to predict the outcomes for both measurement choices precisely. I will explain a recent extension of the uncertainty principle to incorporate this case. The new relation gives a lower bound on the uncertainties, which depends on the amount of entanglement between the particle and the quantum memory. If time permits, I will also outline a couple of applications.

In this talk we will explore a "toy model" of quantum theory that is similar to actual quantum theory, but uses scalars drawn from a finite field. The set of possible states of a system is discrete and finite. Our theory does not have a quantitative notion of probability, but only makes the "modal" distinction between possible and impossible measurement results. Despite its very simple structure, our toy model nevertheless includes many of the key phenomena of actual quantum systems: interference, complementarity, entanglement, nonlocality, and the impossibility of cloning.

We study a Hamiltonian system describing a three-spin 1/2 cluster like interaction competing with an Ising-like exchange. We show that a cluster state, the ground state of the Hamiltonian in the absence of the Ising term, is provided by a hidden order of topological nature. In the presence of the cluster and Ising couplings, a continuous quantum phase transition occurs in the system, directly connecting a local broken symmetry phase to a cluster phase with the hidden order. At the critical point the Hamiltonian is self-dual. We analyze the geometric entanglement and demonstrate that it can capture the transition, as a single parameter.