Abstract
If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. Decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production.
Highlights
Correlations in quantum systems, and in particular entanglement, have been in the focus of research in quantum information science over the past decades
B, decoupled from another system, E, if the joint state of the two systems, ρB E, has product form ρB ρE. This means that the outcome of any measurement on B is statistically independent of the outcome of any measurement on E
The decoupling criterion can be conceptually split into two parts, called achievability and converse part, which we describe informally
Summary
Correlations in quantum systems, and in particular entanglement, have been in the focus of (both theoretical and experimental) research in quantum information science over the past decades. In the context of information theory, this type of argument is, for example, used to analyze state merging [HOW05,HOW07], i.e., the task of conveying a subsystem from a sender to a receiver | who already holds a possibly correlated subsystem | using classical communication and entanglement Another example, where decoupling is used in a similar fashion, is the quantum reverse Shannon theorem [BSST02,BDH+09,BCR11]. While various standard results in quantum information theory have been proved using ideas related to decoupling, the concept came into its own with the discovery of state merging protocols [HOW05,HOW07] and, later, the fully quantum Slepian Wolf protocol [ADHW09] These are based on specific decoupling processes where the mapping T is either a projective measurement or a partial trace.
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