Quantum Mechanics: Axiomatics of Measurements and connections with Computing and Information Retrieval

Memory effects in Quantum Information Theory

  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.

Nilanjana Datta
  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 long-term 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 short-term 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.