Related papers: Complete positivity and correlated neutral kaons
We prove that the linearity and positivity of quantum mechanics impose general restrictions on quantum purification, unveiling a new fundamental limitation of quantum information processing. In particular, no quantum operation can transform…
We prove that checking if a partial matrix is partial totally positive is co-NP-complete. This contrasts with checking a conventional matrix for total positivity, for which we provide a cubic time algorithm. Checking partial sign regularity…
We study k-positive maps on operators. Proofs are given to different positivity criteria. Special attention is on positive maps arising in the study of quantum information science. Results of other researchers are extended and improved. New…
This represents a talk given at the International Conference for Basic Science, July 2025. We review the theory of canonical bases of quantum groups and its relation with the theory of total positivity.
We consider a physical system in which the description of states and measurements follow the usual quantum mechanical rules. We also assume that the dynamics is linear, but may not be fully quantum (i.e unitary). We show that in such a…
"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
A crucial goal of quantum information is to find new ways to exploit the properties of quantum devices as resources. One of the prominent properties of quantum devices of particular interest is their negativity in quasi-probability…
This paper discusses fully coherent quantum feedback control, in which the sensors, controller, and actuators are quantum systems and interact coherently with the system to be controlled: as a result, the entire feedback loop is coherent.…
A necessary condition for reversibility (sufficiency) of a quantum channel with respect to complete families of states with bounded rank is obtained. A full description (up to isometrical equivalence) of all quantum channels reversible with…
Albeit occurring at zero temperature, quantum critical phenomena are known to have a huge impact on the finite-temperature phase diagram of strongly correlated systems -- an aspect which gives experimental access to their observation. In…
We derive a necessary condition for the existence of a completely-positive, linear, trace-preserving map which deterministically transforms one finite set of pure quantum states into another. This condition is also sufficient for…
The kind of information provided by a measurement is determined in terms of the correlation established between observables of the apparatus and the measured system. Using the framework of quantum measurement theory, necessary and…
Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we…
Quantum information can be processed using large ensembles of ultracold and trapped neutral atoms, building naturally on the techniques developed for high-precision spectroscopy and metrology. This article reviews some of the most important…
We consider several applications in black-box quantum computation in which untrusted physical quantum devices are connected together to produce an experiment. By examining the outcome statistics of such an experiment, and comparing them…
The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a…
At quantum critical points (QCP) \cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1 994,Coleman:2005} there are quantum fluctuations on all length scales, from microscopic to macroscopic lengths, which,…
We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the…