Workshop on QUANTUM INFORMATION PROCESSING AND QUANTUM COMMUNICATIONS

Quantum Mechanics: Axiomatics of Measurements
and connections with Computing and Information Retrieval
Memory effects in Quantum Information Theory

aula DOTTORATO  MARTEDI' 25 SETTEMBRE ore 11.00 

NILANJANA
DATTA , University of Cambridge, UK 
>PRESENTATION:
Nilanjana Datta completed her PhD in Mathematical Physics in 1996 at ETH
Zurich. She then held
postdoctoral positions in CNRS Marseille, the Dublin Institute of Advanced
Studies and EPFL, Lausanne. Since 2001, she has been an affiliated lecturer
of the Faculty of Mathematics of the University of Cambridge. She started
her research career by working on problems in Quantum Statistical Mechanics.
Since 2002 she has worked on various aspects of Quantum Information Theory,
including data compression for quantum sources with memory, the additivity
and multiplicativity problems, perfect transfer of quantum states and
entanglement across spin networks, the quantum information spectrum method,
entanglement manipulation and quantum memory channels. She also lectures
a postgraduate course on Quantum Information Theory at the University
of Cambridge.


Abstract 


Optimal rates of quantum information theoretic protocols,
such as compression and transmission of information, and manipulation of
entanglement, were initially obtained under the assumption that the information
source, channel or entanglement resource, used in the protocol, was memoryless.
In real world communication systems, the assumption of sources, channels,
and entanglement resources being memoryless is not always justified. Hence
memory effects need to be taken into account. In this seminar we will focus
attention on memory a effects arising in two different information theoretical
tasks: (1) transmission of classical information through quantum channels,
and (2) manipulating entanglement. We will first consider the transmission
of classical information through a class of channels with longterm memory,
and evaluate its product state capacity. Previous results on capacities
of quantum memory channels were restricted to channels which were \forgetful",
i.e., channels with shortterm memory. Next, we will adopt the powerful
Quantum Information Spectrum method, to compute the classical capacity of
any arbitrary quantum channel. We will then move on to the interesting topic
of entanglement manipulation for arbitrary sequences of states (as opposed
to the known case of i.i.d. sequences of states arising from a memoryless
entanglement resource). We will once again employ the Quantum Information
Spectrum method to evaluate asymptotic entanglement measures, namely the
entanglement cost and the distillable entanglement, for such sequences.
Our results, arising from the use of the Quantum Information Spectrum method,
provide a step in the direction of establishing a unifying mathematical
framework for studying different quantum information protocols, without
making specific assumptions about the nature of the sources, channels or
entanglement resources. A brief summary of this framework and open questions
will be presented. 

