[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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