A reminder of Mark Wilde's talk at 4pm in the Time room at PI.
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