Related papers: Characterising transformations between quantum obj…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
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…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…
Let $H$ and $K$ be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from ${\mathcal B}(H)$ into ${\mathcal B}(K)$ is given, which particularly gives a…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
Quantum instruments are mathematical devices introduced to describe the conditional state change during a quantum process. They are completely positive map valued measures on measurable spaces. We may also view them as non-commutative…
Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a…
Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Entanglement constitutes a key characteristic feature of quantum matter. Its detection, however, still faces major challenges. In this letter, we formulate a framework for probing entanglement based on machine learning techniques. The…
We review some of our recent results (with collaborators) on information processing in an ordered linear spaces framework for probabilistic theories. These include demonstrations that many "inherently quantum" phenomena are in reality quite…
Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may…
Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for…
Quantum decoherence plays a pivotal role in the dynamical description of the quantum-to-classical transition and is the main impediment to the realization of devices for quantum information processing. This paper gives an overview of the…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
One of the most difficult problems in quantum mechanics is the analysis of the measurement processes. In this paper, we point out that many of these difficulties originate from the different roles of measurement outcomes and observable…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…