Quantum Information

Quantum mechanics redefines information and its fundamental properties. Researchers at Perimeter Institute work to understand the properties of quantum information and study which information processing tasks are feasible, and which are infeasible or impossible. This includes research in quantum cryptography, which studies the trade-off between information extraction and disturbance, and its applications. It also includes research in quantum error correction, which involves the study of methods for protecting information against decoherence. Another important side of the field is studying the application of quantum information techniques and insights to other areas of physics, including quantum foundations and condensed matter.

Displaying 853 - 864 of 1338

Algebraic characterization of entanglement classes

Markus Grassl
Max Planck Institute for the Science of Light
September 19, 2014

PIRSA:14090070
Quantum Information
An invariant of topologically ordered states under local unitary transformations

Jeongwan Haah
Massachusetts Institute of Technology (MIT) - Department of Physics
September 10, 2014

PIRSA:14090030
Quantum Information
Strong majorization entropic uncentainty relations

Karol Zyczkowski
Jagiellonian University
July 14, 2014

PIRSA:14070017
Quantum Information
Quantum technologies as tools to deepen our understanding of quantum theory and relativity

Ivette Fuentes
University of Southampton
June 05, 2014

PIRSA:14060006
Quantum Information
The quest for self-correcting quantum memory

Olivier Landon-Cardinal
California Institute of Technology
May 12, 2014

PIRSA:14050028
Quantum Information
Exact Classical Simulation of the Quantum-Mechanical GHZ Distribution

Gilles Brassard
Université de Montréal
April 16, 2014

PIRSA:14040060
Quantum Information
Quantum Computing with Noninteracting Particles

Alex Arkhipov
Massachusetts Institute of Technology (MIT)
April 02, 2014

PIRSA:14040077
Quantum Information
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure

Roger Mong
University of Pittsburgh
March 19, 2014

PIRSA:14030118
Quantum Information
Maximal Privacy Without Coherence

Debbie Leung
Institute for Quantum Computing (IQC)
March 12, 2014

PIRSA:14030105
Quantum Information
Probabilistic protocols in quantum information

Joshua Combes
University of Colorado Boulder
February 13, 2014

PIRSA:14020138
Quantum Information
Applications of Information Theory in Direct Sum and Direct Product Problems
February 12, 2014

PIRSA:14020142
Quantum Information
Bosonic particle-correlated states

Zhang Jiang
University of New Mexico
February 06, 2014

PIRSA:14020135
Quantum Information

Algebraic characterization of entanglement classes

Markus Grassl
Max Planck Institute for the Science of Light
September 19, 2014

PIRSA:14090070
Quantum Information
Entanglement is a key feature of composite quantum system which is directly related to the potential power of quantum computers. In most computational models, it is assumed that local operations are relatively easy to implement. Therefore, quantum states that are related by local operations form a single entanglement class. In the case of local unitary operations, a finite set of polynomial invariants provides a complete characterization of the entanglement classes. Unfortunately, one faces the problem of combinatorial explosion so that computing such a complete set of invariants becomes difficult already for quite small system. The two main problems in this context are to compute invariants and to decide completeness, i.e., whether a given set of invariants generates the full invariant ring. Important tools are both univariate and multivariate Hilbert series which are already difficult to compute. We will also address computational aspects of these problems and techniques for showing completeness of a set of invariants.
An invariant of topologically ordered states under local unitary transformations

Jeongwan Haah
Massachusetts Institute of Technology (MIT) - Department of Physics
September 10, 2014

PIRSA:14090030
Quantum Information
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can compute the topological S-matrix from a single ground state wave function. In this talk, I will show that, for a class of Hamiltonians, it is possible to define the S-matrix regardless of the degeneracy of the ground state. The definition manifests invariance of the S-matrix under local unitary transformations (quantum circuits). The defined S-matrix depends only on the ground state, in the sense that it can be computed by any Hamiltonian in the class of which the state is a ground state. This property, together with the local unitary invariance implies that any quantum circuit that connects two ground states of distinct topological S-matrices must have depth that is at least linear in the diameter of the system. A higher dimensional analog is straightforward. [arXiv:1407.2926]
Strong majorization entropic uncentainty relations

Karol Zyczkowski
Jagiellonian University
July 14, 2014

PIRSA:14070017
Quantum Information
We analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the recent bounds by Coles and Piani, which are known to be stronger than the well known result of Maassen and Uffink. Furthermore, we find a novel bound based on majorization techniques, which also happens to be stronger than the recent results involving largest singular values of submatrices of the unitary matrix connecting both bases. The first set of new bounds give better results for unitary matrices close to the Fourier matrix, while the second one provides a significant improvement in the opposite sectors. Some results derived admit generalization to arbitrary mixed states, so that corresponding bounds are increased by the von Neumann entropy of the measured state. The majorization approach is finally extended to the case of several measurements.
Quantum technologies as tools to deepen our understanding of quantum theory and relativity

Ivette Fuentes
University of Southampton
June 05, 2014

PIRSA:14060006
Quantum Information
Quantum information and quantum metrology can be used to study gravitational effects such as gravitational waves and the universality of the equivalence principle. On one hand, the possibility of carrying out experiments to probe gravity using quantum systems opens an avenue to deepen our understanding of the overlap of these theories. On the other hand, incorporating relativity in quantum technologies promises the development of a new generation of relativistic quantum applications of relevance in Earth-based and space-based setups. In this talk, I will introduce a framework for the application of quantum information and quantum metrology techniques to relativistic quantum fields. I will show how, using this framework, we have been able to develop an accelerometer and a gravitational wave detector which exploit both quantum and relativistic effects. Moreover, our framework can be used to estimate with high precision spacetime parameters such as the Earth's Schwarzchild radius and the gravitational constant.
The quest for self-correcting quantum memory

Olivier Landon-Cardinal
California Institute of Technology
May 12, 2014

PIRSA:14050028
Quantum Information
A self-correcting quantum memory is a physical system whose quantum state can be preserved over a long period of time without the need for any external intervention. The most promising candidates are topological quantum systems which would protect information encoded in their degenerate groundspace while interacting with a thermal environment. Many models have been suggested but several approaches have been shown to fail due to no-go results of increasingly general scope. In a nutshell, 2D topological models and many 3D topological models have point-like excitations which propagate freely and change the groundstate at any non-zero temperature. A recent suggestion is to introduce effective long-range interactions between those point-like excitations. In this presentation, I will first explain the desiderata for self-correction, review the recent advances and no-go results, and describe the current endeavours to define a self-correcting system in 2D and 3D. Time permitting, I will briefly present our recent work on the thermal instability of models which aim to introduce effective long-range interactions between point-like excitations (joint work with Beni Yoshida, John Preskill and David Poulin).
Exact Classical Simulation of the Quantum-Mechanical GHZ Distribution

Gilles Brassard
Université de Montréal
April 16, 2014

PIRSA:14040060
Quantum Information
John Bell has shown that the correlations entailed by quantum mechanics cannot be reproduced by a classical process involving non-communicating parties. But can they be simulated with the help of bounded communication? This problem has been studied for more than twenty years and it is now well understood in the case of bipartite entanglement. However, the issue was still widely open for multipartite entanglement, even for the simplest case, which is the tripartite Greenberger-Horne-Zeilinger (GHZ) state. We give an exact simulation of arbitrary independent von Neumann measurements on general n-partite GHZ states. Our protocol requires O(n^2) bits of expected communication between the parties, and O(n log n) expected time is sufficient to carry it out in parallel. Furthermore, we need only an expectation of O(n) independent unbiased random bits, with no need for the generation of continuous real random variables nor prior shared random variables. In the case of equatorial measurements, we improve earlier results with a protocol that needs only O(n log n) bits of communication and O(log^2 n) parallel time. At the cost of a slight increase in the number of bits communicated, these tasks can be accomplished with a constant expected number of rounds.
Quantum Computing with Noninteracting Particles

Alex Arkhipov
Massachusetts Institute of Technology (MIT)
April 02, 2014

PIRSA:14040077
Quantum Information
We introduce an abstract model of computation corresponding to an experiment in which identical, non-interacting bosons are sent through a non-adaptive linear circuit before being measured. We show that despite the very limited nature of the model, an exact classical simulation would imply a collapse of the polynomial hierarchy. Moreover, under plausible conjectures, a "noisy" approximate simulation would do the same. This gives evidence that quantum computers can sample a distribution that classical computers cannot even approximate, even when restricted to use no entanglement except that arising from particles being identical. We briefly discuss experimental prospects for realizing this model. This talk is based on The Computational Complexity of Linear Optics [STOC '11], which is joint work with Scott Aaronson.
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure

Roger Mong
University of Pittsburgh
March 19, 2014

PIRSA:14030118
Quantum Information
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. The Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support Ising non-Abelian anyons, also referred to as Majorana zero modes. Here we construct a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles, and like the Z3 Read-Rezayi state, harbors Fibonacci anyons that--unlike Ising anyons--allow for universal topological quantum computation solely through braiding.
Maximal Privacy Without Coherence

Debbie Leung
Institute for Quantum Computing (IQC)
March 12, 2014

PIRSA:14030105
Quantum Information
Privacy and coherence have long been considered closely related properties of a quantum state. Indeed, a coherently transmitted quantum state is inherently private. Surprisingly, coherent quantum communication is not always required for privacy: there are quantum channels that are too noisy to transmit quantum information but it can send private classical information. Here, we ask how different the private classical and the quantum capacities can be. We present a class of channels N_d with input dimension d^2, quantum capacity Q(N_d) <= 1, and private classical capacity P(N_d) = log d. These channels asymptotically saturate an interesting inequality P(N) <= (log d_A + Q(N))/2 for any channel N with input dimension d_A, and capture the essence of privacy stripped of the confounding influence of coherence.
Probabilistic protocols in quantum information

Joshua Combes
University of Colorado Boulder
February 13, 2014

PIRSA:14020138
Quantum Information
Probabilistic protocols in quantum information are an attempt to improve performance by occasionally reporting a better result than could be expected from a deterministic protocol. Here we show that probabilistic protocols can never improve performance beyond the quantum limits on the corresponding deterministic protocol. To illustrate this result we examine three common probabilistic protocols: probabilistic amplification, weak value amplification, and probabilistic metrology. In each of these protocols we show explicitly that the optimal deterministic protocol is better than the corresponding probabilistic protocol when the probabilistic nature of the protocol is correctly accounted for.
Applications of Information Theory in Direct Sum and Direct Product Problems
February 12, 2014

PIRSA:14020142
Quantum Information
A fundamental question in complexity theory is how much resource is needed to solve k independent instances of a problem compared to the resource required to solve one instance. Suppose solving one instance of a problem with probability of correctness p, we require c units of some resource in a given model of computation. A direct sum theorem states that in order to compute k independent instances of a problem, it requires k times units of the resource needed to compute one instance. A strong direct product theorem states that, with o(k • c) units of the resource, one can only compute all the k instances correctly with probability exponentially small in k. In this talk, I am going to present some of recent progress on direct sum and direct product theorems in the model of communication complexity and two-prover one-round games with information-theoretic approach. The talk is based on parts of my doctoral work.
Bosonic particle-correlated states

Zhang Jiang
University of New Mexico
February 06, 2014

PIRSA:14020135
Quantum Information
Quantum many-body problems are notorious hard. This is partly because the Hilbert space becomes exponentially big with the particle number N. While exact solutions are often considered intractable, numerous approaches have been proposed using approximations. A common trait of these approaches is to use an ansatz such that the number of parameters either does not depend on N or is proportional to N, e.g., the matrix-product state for spin lattices, the BCS wave function for superconductivity, the Laughlin wave function for fractional quantum Hall effects, and the Gross-Pitaecskii theory for BECs. Among them the product ansatz for BECs has precisely predicted many useful properties of Bose gases at ultra-low temperature. As particle-particle correlation becomes important, however, it begins to fail. To capture the quantum correlations, we propose a new
set of states, which constitute a natural generalization of the product-state ansatz. Our state of N=d& times;n identical particles is derived by symmetrizing the n-fold product of a d-particle quantum state. For fixed d, the parameter space of our state does not grow with N. Numerically, we show that our ansatz gives the right description for the ground state and time evolution of the two-site Bose-Hubbard model.

Title	Speaker(s)	Date	Talk Type	Info link
Algebraic characterization of entanglement classes	Markus Grassl	2014-09-19	Scientific Series	View details
An invariant of topologically ordered states under local unitary transformations	Jeongwan Haah	2014-09-10	Scientific Series	View details
Strong majorization entropic uncentainty relations	Karol Zyczkowski	2014-07-14	Scientific Series	View details
Quantum technologies as tools to deepen our understanding of quantum theory and relativity	Ivette Fuentes	2014-06-05	Scientific Series	View details
The quest for self-correcting quantum memory	Olivier Landon-Cardinal	2014-05-12	Scientific Series	View details
Exact Classical Simulation of the Quantum-Mechanical GHZ Distribution	Gilles Brassard	2014-04-16	Scientific Series	View details
Quantum Computing with Noninteracting Particles	Alex Arkhipov	2014-04-02	Scientific Series	View details
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure	Roger Mong	2014-03-19	Scientific Series	View details
Maximal Privacy Without Coherence	Debbie Leung	2014-03-12	Scientific Series	View details
Probabilistic protocols in quantum information	Joshua Combes	2014-02-13	Scientific Series	View details
Applications of Information Theory in Direct Sum and Direct Product Problems		2014-02-12	Scientific Series	View details
Bosonic particle-correlated states	Zhang Jiang	2014-02-06	Scientific Series	View details

Quantum Information

Format results