Hi all,
next week, we have a talk by Mark Wilde on Wednesday at 4pm in the
Time Room.
Best wishes,
Markus
Title:
The information-theoretic costs of simulating quantum
measurements
Speaker: Mark Wilde (McGill University)
Abstract:
Winter's measurement compression theorem stands as one of the most
important, yet perhaps less well-known coding theorems in quantum
information theory. Not only does it make an illuminative statement
about measurement in quantum theory, but it also underlies several
other general protocols used for entanglement distillation or local
purity distillation. The theorem provides for an asymptotic
decomposition of any quantum measurement into an "extrinsic" source
of noise, classical noise in the measurement that is independent of
the actual outcome, and "intrinsic" quantum noise that can be due in
part to the nonorthogonality of quantum states. This decomposition
leads to an optimal protocol for a sender to 1) simulate many
instances of a quantum measurement acting on many copies of some
state and 2) send the outcomes of the measurements to a receiver
using as little classical communication as possible while still
having a faithful simulation. The protocol assumes that the parties
have access to some amount of common randomness, which is a strictly
weaker resource than classical communication.
In this talk, we provide a full review of Winter's measurement
compression theorem, detailing the information processing task,
providing examples for understanding it, overviewing Winter's
achievability proof, and detailing a new approach to its
single-letter converse theorem. We then overview the
Devetak-Winter theorem on classical data compression with quantum
side information, providing new proofs of the achievability and
converse parts of this theorem. From there, we outline a new
protocol that we call "measurement compression with quantum side
information," a protocol announced in prior work on trade-offs in
quantum Shannon theory. This protocol has several applications,
including its part in the "classically-assisted state
redistribution" protocol, which is the most general protocol on
the static side of the quantum information theory tree, and its
role in reducing the classical communication cost in a task known
as local purity distillation. We finally outline a connection
between this protocol and recent work on entropic uncertainty
relations in the presence of quantum memory.
This is joint with Patrick Hayden, Francesco Buscemi, and
Min-Hsiu Hsieh.
Date: April 18, 2012 - 4:00 pm
Series: Perimeter Institute Quantum Discussions
Location: Time Rm