This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
It is well known that the ground state energy of many-particle Hamiltonians involving only 2- body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are 'N-representable' is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle pre-image, satisfying a conjecture established in 1972.
Quantum Mechanics has been shown to provide a rigorous foundation for Statistical Mechanics. Concentration of measure, or typicality, is the main tool to construct a purely quantum derivation for the methods of Statistical Mechanics. From this point of view statistical ensembles are effective description for isolated quantum systems, since typically a random pure state of the system will have properties similar to those of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are not relevant for realistic systems.
I'll describe a connection between uncertainty relations, information locking and low-distortion embeddings of L2 into L1. Exploiting this connection leads to the first explicit construction of entropic uncertainty relations for a number of measurements that is polylogarithmic in the dimension d while achieving an average measurement entropy of (1-e) log d for arbitrarily small e. From there, it is straightforward to obtain the first strong information locking scheme that is efficiently computable using a quantum computer.
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.
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.
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.
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.
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.
In this talk I review some joint work (arXiv:1008.2147) with Bill Munro and Tim Spiller on the task we call "quantum tagging", that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is unbounded. Simple security models for this task will be presented.
Fibonacci anyons are the simplest system of anyons capable of implementing universal topological quantum computation, an area which is of intense theoretical and experimental interest. Recent studies have shown that for nearest-neighbour interactions, the properties of the ground state of a 1-D chain of Fibonacci anyons may be modeled using a spin chain, and are related to specific conformal field theories.