Related papers: Covariant quantum combinatorics with applications …
Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently…
Quantum operations, or quantum channels cannot be inverted in general. An arbitrary state passing through a quantum channel looses its fidelity with the input. Given a quantum channel ${\cal E}$, we introduce the concept of its…
We demonstrate that a quantum graph exhibits a $\mathcal{PT}$-symmetry provided the coefficients in the condition describing the wave function matching at the vertices are circulant matrices; this symmetry is nontrivial if they are not…
This note introduces a family of circulant quantum channels -- a subclass of the mixed-permutation channels -- and investigates its key structural and operational properties. We show that the image of the circulant quantum channel is…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various physical settings. Quantum channels…
Information theory establishes the ultimate limits on performance for noisy communication systems [Shannon48]. An accurate model of a physical communication device must include quantum effects, but typically including these makes the theory…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
Quantum symmetry of a graph $C^{*}$-algebra $C^{*}(\Gamma)$ corresponding to a finite graph $\Gamma$ has been explored by several mathematicians within different categories in the past few years. In this article, we establish that there are…
We investigate the semigroup structure of bosonic Gaussian quantum channels. Particular focus lies on the sets of channels which are divisible, idempotent or Markovian (in the sense of either belonging to one-parameter semigroups or being…
Quantum capacity, as the key figure of merit for a given quantum channel, upper bounds the channel's ability in transmitting quantum information. Identifying different type of channels, evaluating the corresponding quantum capacity and…
This article comprehensively explores matrices and their prerequisites for achieving positive semidefiniteness. The study delves into a series of theorems concerning pure quantum states in the context of weighted graphs. The main objective…
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the…
No quantum circuit can turn a completely unknown unitary gate into its coherently controlled version. Yet, coherent control of unknown gates has been realised in experiments, making use of a different type of initial resources. Here, we…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
We introduce a formulation of gauge theory on noncommutative spaces based on the concept of covariant coordinates. Some important examples are discussed in detail. A Seiberg-Witten map is established in all cases.
This work is at the interface of graph theory and quantum mechanics. Quantum correlations epitomize the usefulness of quantum mechanics. Quantum discord is an interesting facet of bipartite quantum correlations. Earlier, it was shown that…