エンタングルメントの漸近的変換可能性：エンタングルメント蒸留と希釈における一般的アプローチ

電気通信大学201

State convertibility in the von Neumann algebra framework

We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite von Neumann algebras. Namely, we establish a generalisation to this setting of Nielsen's theorem on the convertibility of quantum states under local operations and classical communication (LOCC) schemes. Along the way, we introduce an appropriate generalisation of LOCC operations and connect the resulting notion of approximate convertibility to the theory of singular numbers and majorisation in von Neumann algebras. As an application of our result in the setting of $II_1$-factors, we show that the entropy of the singular value distribution relative to the unique tracial state is an entanglement monotone in the sense of Vidal, thus yielding a new way to quantify entanglement in that context. Building on previous work in the infinite-dimensional setting, we show that trace vectors play the role of maximally entangled states for general $II_1$-factors. Examples are drawn from infinite spin chains, quasi-free representations of the CAR, and discretised versions of the CCR.Comment: 36 pages, v2: journal version, 38 page

Complete classification of steerability under local filters and its relation with measurement incompatibility

Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples

Entanglement and Decoherence: Mathematics and Physics of Quantum Information and Computation

This is the report for the Oberwolfach workshop on Entanglement and Decoherence: Mathematics and Physics, held January 23 - 29, 2005

Bipartite Quantum Interactions: Entangling and Information Processing Abilities

The aim of this thesis is to advance the theory behind quantum information processing tasks, by deriving fundamental limits on bipartite quantum interactions and dynamics, which corresponds to an underlying Hamiltonian that governs the physical transformation of a two-body open quantum system. The goal is to determine entangling abilities of such arbitrary bipartite quantum interactions. Doing so provides fundamental limitations on information processing tasks, including entanglement distillation and secret key generation, over a bipartite quantum network. We also discuss limitations on the entropy change and its rate for dynamics of an open quantum system weakly interacting with the bath. We introduce a measure of non-unitarity to characterize the deviation of a doubly stochastic quantum process from a noiseless evolution. Next, we introduce information processing tasks for secure read-out of digital information encoded in read-only memory devices against adversaries of varying capabilities. The task of reading a memory device involves the identification of an interaction process between probe system, which is in known state, and the memory device. Essentially, the information is stored in the choice of channels, which are noisy quantum processes in general and are chosen from a publicly known set. Hence, it becomes pertinent to securely read memory devices against scrutiny of an adversary. In particular, for a secure read-out task called private reading when a reader is under surveillance of a passive eavesdropper, we have determined upper bounds on its performance. We do so by leveraging the fact that private reading of digital information stored in a memory device can be understood as secret key agreement via a specific kind of bipartite quantum interaction.Comment: PhD Thesis (minor revision). Also available at: https://digitalcommons.lsu.edu/gradschool_dissertations/4717

Values of cooperative quantum games

We develop a resource-theoretical approach that allows us to quantify values of two-player, one-round cooperative games with quantum inputs and outputs, as well as values of quantum probabilistic hypergraphs. We analyse the quantum game values arising from the type hierarchy of quantum no-signalling correlations, establishing tensor norm expressions for each of the correlation types. As a consequence, we provide metric characterisations of state convertibility via LOSR and LOCC.En route, we obtain an alternative description of the maximal tensor products of ternary rings of operators.Comment: 60 page