554,951 research outputs found
Subfactors and quantum information theory
We consider quantum information tasks in an operator algebraic setting, where
we consider normal states on von Neumann algebras. In particular, we consider
subfactors , that is, unital inclusions of
von Neumann algebras with trivial center. One can ask the following question:
given a normal state on , how much can one learn by only
doing measurements from ? We argue how the Jones index
can be used to give a quantitative answer to
this, showing how the rich theory of subfactors can be used in a quantum
information context. As an example we discuss how the Jones index can be used
in the context of wiretap channels.
Subfactors also occur naturally in physics. Here we discuss two examples:
rational conformal field theories and Kitaev's toric code on the plane, a
prototypical example of a topologically ordered model. There we can directly
relate aspects of the general setting to physical properties such as the
quantum dimension of the excitations. In the example of the toric code we also
show how we can calculate the index via an approximation with finite
dimensional systems. This explicit construction sheds more light on the
connection between topological order and the Jones index.Comment: v2: added more background material, some corrections and
clarifications. 23 pages, submitted to QMath 13 (Atlanta, GA) proceeding
Languages of Quantum Information Theory
This note will introduce some notation and definitions for information
theoretic quantities in the context of quantum systems, such as (conditional)
entropy and (conditional) mutual information. We will employ the natural
C*-algebra formalism, and it turns out that one has an allover dualism of
language: we can define everything for (compatible) observables, but also for
(compatible) C*-subalgebras. The two approaches are unified in the formalism of
quantum operations, and they are connected by a very satisfying inequality,
generalizing the well known Holevo bound. Then we turn to communication via
(discrete memoryless) quantum channels: we formulate the Fano inequality, bound
the capacity region of quantum multiway channels, and comment on the quantum
broadcast channel.Comment: 16 pages, REVTEX, typos corrected, references added and extende
Recoverability in quantum information theory
The fact that the quantum relative entropy is non-increasing with respect to
quantum physical evolutions lies at the core of many optimality theorems in
quantum information theory and has applications in other areas of physics. In
this work, we establish improvements of this entropy inequality in the form of
physically meaningful remainder terms. One of the main results can be
summarized informally as follows: if the decrease in quantum relative entropy
between two quantum states after a quantum physical evolution is relatively
small, then it is possible to perform a recovery operation, such that one can
perfectly recover one state while approximately recovering the other. This can
be interpreted as quantifying how well one can reverse a quantum physical
evolution. Our proof method is elementary, relying on the method of complex
interpolation, basic linear algebra, and the recently introduced Renyi
generalization of a relative entropy difference. The theorem has a number of
applications in quantum information theory, which have to do with providing
physically meaningful improvements to many known entropy inequalities.Comment: v5: 26 pages, generalized lower bounds to apply when supp(rho) is
contained in supp(sigma
Alternative new notation for quantum information theory
A new notation has been introduced for the quantum information theory. By
this notation,some calculations became simple in quantum information theory
such as quantum swapping, quantum teleportation.Comment: submitte
- …