[quantum-info] Today's PIQuDos
Markus Mueller
markus14m at gmail.com
Wed Apr 18 08:53:37 EDT 2012
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
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