3 research outputs found
Singular value decomposition and matrix reorderings in quantum information theory
We review Schmidt and Kraus decompositions in the form of singular value
decomposition using operations of reshaping, vectorization and reshuffling. We
use the introduced notation to analyse the correspondence between quantum
states and operations with the help of Jamiolkowski isomorphism. The presented
matrix reorderings allow us to obtain simple formulae for the composition of
quantum channels and partial operations used in quantum information theory. To
provide examples of the discussed operations we utilize a package for the
Mathematica computing system implementing basic functions used in the
calculations related to quantum information theory.Comment: 11 pages, no figures, see
http://zksi.iitis.pl/wiki/projects:mathematica-qi for related softwar
Information gain and measurement disturbance for quantum agents
The traditional formalism of quantum measurement (hereafter ``TQM'')
describes processes where some properties of quantum states are extracted and
stored as classical information. While TQM is a natural and appropriate
description of how humans interact with quantum systems, it is silent on the
question of how a more general, quantum, agent would do so. How do we describe
the observation of a system by an observer with the ability to store not only
classical information but quantum states in its memory? In this paper, we
extend the idea of measurement to a more general class of sensors for quantum
agents which interact with a system in such a way that the agent's memory
stores information (classical or quantum) about the system under study. For
appropriate sensory interactions, the quantum agent may ``learn'' more about
the system than would be possible under any set of classical measurements --
but as we show, this comes at the cost of additional measurement disturbance.
We experimentally demonstrate such a system and characterize the tradeoffs,
which can be done by considering the information required to erase the effects
of a measurement