Related papers: Covariant quantum combinatorics with applications …
Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are…
We study the quantum channel version of Shannon's zero-error capacity problem. Motivated by recent progress on this question, we propose to consider a certain operator space as the quantum generalisation of the adjacency matrix, in terms of…
Quantum communication theory focuses on the study of quantum channels for transmitting quantum information, where the transmission rate is measured by quantum channel capacity. This quantity exhibits several intriguing properties, such as…
We show that unbounded number of channel uses may be necessary for perfect transmission of quantum information. For any n we explicitly construct low-dimensional quantum channels ($d_A$=4, $d_E$=2 or 4) whose quantum zero-error capacity is…
As with classical information, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels. In contrast to the classical theory, imperfect quantum channels exhibit a strong kind of synergy:…
A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional…
We introduce a class of linear maps irreducibly covariant with respect to the finite group generated by the Weyl operators. This group provides a direct generalization of the quaternion group. In particular, we analyze the irreducibly…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues…
We define the coherence non-generating channel as the completely positive trace-preserving map which does not generate quantum coherence from an incoherent state. The incoherent operations are the strict subset of the coherence…
In this thesis, we explore the intersection of two fundamental subfields of quantum information theory: quantum coherence and contextuality. Despite their apparent differences, both areas address key issues relevant to the foundations and…
We present covariant quantization rules for nonsingular finite dimensional classical theories with flat and curved configuration spaces. In the beginning, we construct a family of covariant quantizations in flat spaces and Cartesian…
Operational contextuality forms a rapidly developing subfield of quantum information theory. However, the characterization of the quantum mechanical entities that fuel the phenomenon has remained unknown with many partial results existing.…
Coherence is a basic notion for quantum states. Instead of quantum states, in this work, We establish a resource theory for quantifying the coherence of Gaussian channels. To do this, we propose the definitions of incoherent Gaussian…
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial…
Compatibility conditions of quantum channels featuring symmetry through covariance are studied. Compatibility here means the possibility of obtaining two or more channels through partial trace out of a broadcasting channel. We see that…
We report a method that exploits a connection between quantum contextuality and graph theory to reveal any form of quantum contextuality in high-precision experiments. We use this technique to identify a graph which corresponds to an…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…