One of the most profound insights of the Choi-Jamio lkowski isomorphism is that
quantum processes can be treated as quantum states. Following this idea, it is
natural to consider a kind of super-processes that transform quantum processes into
quantum processes, in a similar way as ordinary processes transform quantum states
into quantum states. This construction can be iterated...
I discuss the interplay between Physics and Mathematics, from a personal perspective, in the light of the celebrated Choi-Jamio lkowski Isomorphism. I argue that it is desirable that a physical law, when expressed in terms of a differential equation, should admit any initial conditions. Choi-Jamio lkowski isomorphism, complete positivity, correlations and entanglement form a facet pattern that...
We first study generalizations of Choi matrices for linear maps of the n×n matrices
into themselves. Then we generalize this to certain maps of Von Neumann algebras
into themselves.
Despite its long history, research in open quantum dynamics still provides unexpected facets. We shall discuss some of them that are connected with entanglement generation and super-activation of back-flow of information by means of tensor products of dynamical maps.
Finite Heisenberg groups have a certain universal status. In every finite dimensional
Hilbert space there is at least one Heisenberg group that acts irreducibly in this
dimension, and in no other. I will describe some dimension dependent structures
that arise in this way, and some connections between seemingly different dimensions
that arise from them.
In this talk, I will provide a generic version of quantum Wielandt’s inequality, which
gives an optimal upper bound on the minimal length such that products of that
length of n-dimensional matrices in a generating system span the whole matrix
algebra with probability one. I will show that this length generically is of order
Θ(log n), as opposed to the general case, in which the best bound...
I use an operational formulation of the Choi-Jamio lkowski isomorphism to explore
an approach to quantum mechanics in which the state is not the fundamental ob-
ject. I first situate this project in the context of generalized probabilistic theories
and argue that this framework may be understood as a means of drawing conclusions
about the intratheoretic causal structure of quantum...
Understanding how positivity of maps behaves under tensor products is linked to
several open problems in quantum information theory. In my talk, I will present
some recent results on how non-decomposable positive maps can arise from tensor
products and tensor powers of decomposable maps. The Choi-Jamio lkowski isomorphism is an indispensable tool in this line of research.
We introduce an experimentally accessible network representation for many-body
quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain
model, the XX model, and showing that it brings to light new phenomena. The
analysis of these entanglement networks reveals that the gradual...
Partially motivated by recent research in quantum physics, we take a closer look
at the similarities and differences between the study of positive maps, separability,
and entanglement in the real and complex case. It is possible for real matrices to
be entangled as operators on a real Hilbert space and yet separable when regarded
as acting on a complex space. These two distinct theories of...
