IQI: Institute for Quantum Information Weekly Seminars
We invite experts to our weekly IQI Seminar Series to tell us about their recent research advances. We also hold more informal group meetings and sponsor IQI Workshops from time to time. Below is a calendar of these and other events of interest to the IQI community.
Debbie Leung, Perimeter
Tuesday, April 21, 2015 3:00 p.m. 107 Annenberg
Operationally-Motivated Uncertainty Relations for Joint Measurability and the Error-Disturbance Tradeoff
Volker Scholz, ETH
Tuesday, March 24, 2015 3:00 p.m. 107 Annenberg
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error- disturbance tradeoff for arbitrary observables of finite-dimensional systems (I will shortly mention the extension to position/momentum). The relations are formulated in terms of a directly operational quantity, namely the probability of distinguishing the actual operation of a device from its hypothetical ideal, by any possible testing procedure whatsoever. Moreover, they may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment.
Joint work with Joe Renes and Stefan Huber, ETH Zurich, based on arXiv:1402.6711
Quantum systems with approximation-robust entanglement
Lior Eldar, MIT
Tuesday, March 17, 2015 3:00 p.m. 107 Annenberg
Quantum entanglement is considered, by and large, to be a very delicate and nonrobust phenomenon, that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest for a quantum analog of the PCP theorem, researches have tried to establish whether or not we can preserve quantum entanglement at ”constant” temperatures that are independent of system size. This would imply that any quantum state with energy at most, say 0.05 of the total available energy of the Hamiltonian, would be highly-entangled. However to date, no such systems were found, and moreover, it became evident that even embedding local Hamiltonians on robust, albeit ”non-physical” topologies, namely expanders, does not guarantee entanglement robustness. In this talk, we will try to indicate that such robustness may be possible after all, by slightly relaxing the approximation condition, in a way that is reminiscent of classical approximation problems. Instead of asking that any quantum state with fractional energy at most 0.05 be highly-entangled, we just ask that any quantum state violating a fraction at most 0.05 of constraints is highly-entangled. I will then construct an infinite family of (logarithmically)-local Hamiltonians, with the following property of such combinatorial inapproximability: any quantum state that violates a fraction at most 0.05 of all local terms cannot be even approximately simulated by classical circuits whose depth is logarithmic. Alternatively, this will show that in a system of n qubits, it is possible to enforce a robust form of entanglement on the order of sqrt(n) qubits, using quantum constraints whose support is polylog(n). Several open questions follow from this construction that are related both to previous approximability results, the definition of entanglement-robust systems called NLTS, quantum locally testable codes, linear distance LDPC codes, and quantum circuit lower bounds.
Two little results in topology, motivated by quantum computation
Gorjan Alaic, University of Copenhagen
Tuesday, March 10, 2015 3:00 p.m. 107 Annenberg
Quantum computation has taken much from the scientific fields it sprouted from. Occasionally, it has also given back. I will discuss two recent results, both of which employ basic methods and ideas from quantum computation to prove a new theorem about low-dimensional topology. In the first result, we show the existence of 3-manifold diagrams which cannot be made ``very thin'' via local transformations. The key to the proof is establishing the #P-hardness of certain 3-manifold invariants, which we achieve via an application of the Solovay-Kitaev universality theorem with exponential precision. In the second result, we prove a relationship between the distinguishing power of a link invariant, and the entangling power of the linear operator that describes braiding. More precisely, we show that link invariants derived from non-entangling solutions to the Yang-Baxter equation are trivial. The former is joint work with Catharine Lo (Caltech), and the latter is joint work with Stephen Jordan and Michael Jarett (UMD).
Characterizing Topological Order with Matrix Product Operators
Burak Sahinoglu, Universitat Wien
Tuesday, February 17, 2015 3:00 p.m. 107 Annenberg
In this talk, we focus on describing topologically ordered ground state spaces of local Hamiltonians. This description includes a set of rules (tensor equations) which are satisfied by a matrix product operator (MPO) and the local tensor of the tensor network state (TNS). We see that these rules are satisfied for string-net models by showing that the consistency equations for these models correspond to our set of rules for a specific local tensor and MPO. At the end, we will discuss possible future directions.
Topological quantum computation with anyons
Claire Levaillant, UCSB
Tuesday, February 10, 2015 3:00 p.m. 107 Annenberg
We present computational schemes available at SU(2)_4 for universal quantum computation.
Phase transitions in non-Abelian string nets
Julien Vidal, Laboratoire de Physique de la Matière Condensée
CNRS/Université Pierre et Marie Curie, Paris
Tuesday, February 3, 2015 3:00 p.m. 107 Annenberg
Phase transitions in topologically ordered systems remain a widely unexplored domain mainly due to the lack of theoretical tools to analyze them. In the absence of effective field theory, microscopic models are important to investigate the possible condensation mechanisms driving transitions. In this context, the string-net model introduced ten years ago by M. Levin and X.-G. Wen is especially attractive since it allows to study any (doubled achiral) topological phase. In the absence of perturbation, string-net condensates can be seen as deconfined phases in which excitations are anyons. In this talk, I will discuss the influence of a string tension in non-Abelian string-net models and I will show that it leads to phase transitions which depend on the anyon theory considered. I will also address the issue of anyonic bound states that may be generated by this string tension and their possible relevance to understand the nature of the phase transitions.
Wigner functions negativity and contextuality in quantum computation
Nicolas Delfosse, Sherbrooke
Tuesday, January 27, 2015 3:00 p.m. 107 Annenberg
One of the most common way to obtain universality in quantum computation is by the injection of magic states. This raises the question: Which quantum properties of these states are responsible for the gain in computational power? Wigner functions negativity and contextuality have recently been proposed to explain this extra power for qupits (p-level systems for odd p). Unfortunately the case of qubits seems much more involved. In this talk, I will recall the construction of Discrete Wigner functions and their relation with contextuality and quantum computation for qupits. Then I will consider the case of real 2-level systems and I will explain how to resurrect most of the previous results. This is a first step toward qubits.
Based on joint work with Philippe Allard Guerin, Jacob Bian and Robert Raussendorf. http://arxiv.org/abs/1409.5170
Verifying entanglement in physical systems
Dvir Kafri, JQI
Tuesday, January 6, 2015 3:00 p.m. 107 Annenberg
Interactions consistent with Lorentz invariance are fundamentally local, with non-local force laws arising once we “integrate out” the force carriers. Since at a local level quantum mechanics describes reality very well, this brings up the question of why we observe classical behavior at most macroscopic length scales. In this talk, I argue that classical behavior could be due to an inability of the force carriers to convey entanglement, and provide a model describing how this comes about. The model gives a local test that allows one to verify that entanglement has been generated, falsifying the classical hypothesis. Crucially, the local test allows noise measurements to directly verify entanglement generation. I then describe applications of these test in the context of the gravitational force, measurement and feedback, and simulated many-body systems.
Information Causality, Szemeredi-Trotter, and algebraic variants
Mohammad Bavarian, MIT
Tuesday, November 18, 2014, 3:00 p.m. 107 Annenberg
In this work, we consider the following family of two prover one-round games. In the CHSH_q game, two parties are given x,y in F_q uniformly at random, and each must produce an output a,b in F_q without communicating with the other. The players' objective is to maximize the probability that their outputs satisfy a+b=xy in F_q. This game was introduced by Buhrman and Massar (PRA 2005) as a large alphabet generalization of the celebrated CHSH game---which is one of the most well-studied two-prover games in quantum information theory, and which has a large number of applications to quantum cryptography and quantum complexity. Our main contributions in this paper are the first asymptotic and explicit bounds on the entangled and classical values of CHSH_q, and the realization of a rather surprising connection between CHSH_q and geometric incidence theory. On the way to these results, we also resolve a problem of Pawlowski and Winter about pairwise independent Information Causality, which, beside being interesting on its own, gives as an application a short proof of our upper bound for the entangled value of CHSH_q.
Joint work with Peter W. Shor.
Entanglement in one-dimensional quantum systems
Yichen Huang, UC Berkeley
Tuesday, October 14, 2014, 3:00 p.m. 107 Annenberg
Quantum entanglement, a concept from quantum information theory, has been widely used in condensed matter physics to characterize quantum correlations that are difficult to study using conventional methods. It provides unique insights into the physics of critical states and topological order. It is also quantitatively related to the difficulty of describing ground states using matrix-product-state representations in numerical approximations. In this talk, I will discuss some recent examples in these directions in the context of 1D quantum systems. I will focus on conceptual messages rather than technical perspectives.
Area law: Starting with a review of known rigorous results on the relation between gapped states, correlation decay, area law, and efficient matrix-product-state representations, I will discuss area law for Renyi entropy and possible generalizations in the presence of ground-state degeneracy.
Entanglement and topological order: It is argued that topological order is essentially a pattern of long-range entanglement. I will discuss a quantitative characterization of long-range entanglement using local quantum circuits. In particular, I will show that to generate a topologically ordered state from a product state a local quantum circuit of linear (in system size) depth is necessary and (up to small errors) sufficient.
Entanglement in critical disordered systems: Many-body localization studies how disorder leads to localized states in strongly correlated systems. It is a property associated with all eigenstates (not just the ground state) of disordered systems. I will show how to use entanglement for probing the singularities of all eigenstates.
For a complete listing of IQI seminars from 2001 through April 2012, see the archived IQI web page