Théorie de l'information quantique
Org: Richard Cleve (Waterloo)
- GILAD GOUR, University of Calgary, Department of Mathematics and
Statistics, Calgary, Alberta
Quantum Resource Theories and Super Selection Rules
In quantum information theory entanglement arises due to the
restriction to local operations and classical communication (LOCC).
In particular, entanglement can be considered as a quantum resource
with which spatially separated parties can overcome or at least partly
overcome the limitation of LOCC. Clearly, different types of
restrictions corresponds to different kinds of quantum resource
theories (QRTs). In this talk I will discuss the QRTs that emanate
from various natural constraints. I will focus on QRTs that follow
from the presence of super-selection rules or the absence of shared
reference frames. In particular, I will discuss the analogies and
distinctions between and among the different QRTs and show that, in
general, QRTs in many aspects are very similar to entanglement theory.
Such comparisons provide a much broader perspective on all of these
resource theories and allow us to use the insights gained from one QRT
to solve the problems that arise in the context of another QRT.
Joint work with Rob Spekkens.
- PATRICK HAYDEN, McGill University
A reverse Shannon theorem for quantum broadcast channels
A reverse Shannon theorem characterizes the resources required to
simulate a given noisy channel. The quantum reverse Shannon theorem
for single-sender/single-receiver channels, a joint effort of Bennett,
Devetak, Harrow, Shor and Winter, established that a single number can
be used to characterize the strength of such channels in the presence
of free entanglement. In this talk I'll explain how to prove an
optimal reverse Shannon theorem for quantum channels with a single
sender but many receivers, known as broadcast channels. Surprisingly,
the simulation cost for a broadcast channel can be characterized by a
simple, tractable optimization problem even though no such simple
solution has been found for the capacity region itself, even in the
Joint work with Frederic Dupuis.
- DEBBIE LEUNG, University of Waterloo
Approximate error correction
We will discuss a construction based on quantum list-codes, and its
application to adversarial quantum channels.
Joint work with Graeme Smith.
- AIDAN ROY, University of Calgary, 2500 University Drive NW, Calgary,
AB, T2N 1N4
Weighted complex projective 2-designs from bases
We introduce the problem of constructing weighted complex projective
2-designs from the union of a family of orthonormal bases. If the
weight remains constant across elements of the same basis, then such
designs can be interpreted as generalizations of complete sets of
mutually unbiased bases, being equivalent whenever the design is
composed of d+1 bases in dimension d. We show that, for the
purpose of quantum state determination, these designs specify an
optimal collection of orthogonal measurements. Using highly nonlinear
functions on abelian groups, we construct explicit examples from d+2
orthonormal bases whenever d+1 is a prime power, covering dimensions
d+d=6, 10, and 12, for example, where no complete sets of
mutually unbiased bases have thus far been found.
This is joint work with Andrew Scott.
- BARRY SANDERS, University of Calgary, 2500 University Drive NW, Calgary,
AB, T2N 1N4
Information-theoretic security for authenticated
long-distance quantum key distribution with partial trust
Quantum key distribution must overcome two important hurdles:
authentication to avoid the man-in-the-middle attack and relays or
repeaters to allow long-distance communication. Current feasible
approaches suggest complete trust of intermediate nodes in a network.
We show that, in a network of partially trusted nodes (even with a low
level of trust), our scheme enables probabilistic
information-theoretic secure authentication and long-distance key
distribution based on existing quantum key distribution technology,
thus making our approach feasible now without reliance on total trust
of intermediate nodes.
- ALAIN TAPP, Université de Montréal
Anonymous message transmission
Anonymous message transmission is the task by which a sender transmits
to a receiver a private message in such a way that the receiver does
not know who, within the user group, actually sent the message.
Furthermore, the rest of the users do not learn anything. The case
involving classical messages has been recently solved by A. Broadbent
and A. Tapp. They have proposed an information theoretically secure
protocol, based solely on pairwise authentic private channels, that
tolerates an arbitrary number of corrupted players. I will present a
protocol that accomplishes the same goal, in the same model, but with
This work has been done in collaboration with G. Brassard,
A. Broadbent, J. Fitzsimons and S. Gambs.