Related papers: On the Choi-Jamiolkowski Correspondence in Infinit…
We consider a nontrivial class of infinite dimensional quantum channels characterized by finiteness of the Holevo capacity. Some general properties of channels of this class are described. In particular, a special sufficient condition of…
We investigate whether sequential unitary circuits can prepare two-dimensional chiral states, using a correspondence between sequentially prepared states, isometric tensor network states, and one-dimensional quantum channel circuits. We…
We present two projects concerning the main part of my PhD work. In the first one we study quantum channels, which are the most general operations mapping quantum states into quantum states, from the point of view of their divisibility…
It is easy to show coincidence of the entanglement-assisted classical capacity and the Holevo capacity for any c-q channel between finite dimensional quantum systems. In this paper we prove the converse assertion: coincidence of the…
An infinite-dimensional version of Calogero-Moser operator of $BC$-type and the corresponding Jacobi symmetric functions are introduced and studied, including the analogues of Pieri formula and Okounkov's binomial formula. We use this to…
In this paper we introduce the notion of infinite dimensional Jacobi structure to describe the geometrical structure of a class of nonlocal Hamiltonian systems which appear naturally when applying reciprocal transformations to Hamiltonian…
We develop an approximation approach to infinite dimensional quantum channels based on detailed investigation of the continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely…
By using the Choi-Jamio{\l}kowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched R\'{e}nyi relative entropy. Elegant properties of the…
Entanglement breaking (EB) channels, as completely positive and trace-preserving linear operators, sever the entanglement between the input system and other systems. In the realm of infinite-dimensional systems, a related concept known as…
We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can…
Sending quantum information reliably over long distances is a central challenge in quantum technology in general, and in quantum optics in particular, since most quantum communication relies on optical fibres or free-space links. Here, we…
We provide a one-to-one correspondence between line operators and states in four-dimensional CFTs with continuous 1-form symmetries. In analogy with 0-form symmetries in two dimensions, such CFTs have a free photon realisation and enjoy an…
We develop the theory of quantum (a.k.a. noncommutative) relations and quantum (a.k.a. noncommutative) graphs in the finite-dimensional covariant setting, where all systems (finite-dimensional $C^*$-algebras) carry an action of a compact…
In this paper we state a one-to-one connection between the maximal ratio of the circumradius and the diameter of a body (the Jung constant) in an arbitrary Minkowski space and the maximal Minkowski asymmetry of the complete bodies within…
Bosonic channels are important in practice as they form a simple model for free-space or fiber-optic communication. Here we consider a single-sender two-receiver pure-loss bosonic broadcast channel and determine the unconstrained capacity…
A unit-preserving and completely positive linear map, or a channel, $\Lambda \colon \mathcal{A} \to \mathcal{A}_{\mathrm{in}}$ between $C^\ast$-algebras $\mathcal{A}$ and $\mathcal{A}_{\mathrm{in}}$ is called entanglement-breaking (EB) if…
We consider fundamental limits for communicating over a compound channel when the state of the channel needs to be masked. Our model is closely related to an area of study known as covert communication that is a setting in which the…
We study methods of inducing metrics on unital completely positive maps by employing seminorms arising in noncommutative geometry. Our main approach relies on the development of an infinite-dimensional $C^*$-algebraic analogue of the…
In this paper we present a novel quasi-exactly solvable model with symmetric inverted potentials which are unbounded from below. The quasi-exactly solvable states are shown to be total transmission (or reflectionless) modes. From these…
A pure-loss bosonic channel is a simple model for communication over free-space or fiber-optic links. More generally, phase-insensitive bosonic channels model other kinds of noise, such as thermalizing or amplifying processes. Recent work…