Related papers: The inverse eigenvalue problem for quantum channel…
If a sender and a receiver lack precise knowledge about the communication line that connects them, designing a scheme to reliably transmit information becomes more challenging. This has been studied in classical and quantum information…
Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. By using $\rho$-absolute variance, we introduce the uncertainty of quantum…
To determine if two lists of numbers are the same set, we sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms arise in graph isomorphism…
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…
A formula for the capacity of a quantum channel for transmitting private classical information is derived. This is shown to be equal to the capacity of the channel for generating a secret key, and neither capacity is enhanced by forward…
The one-shot zero-error classical capacity of a quantum channel is the amount of classical information that can be transmitted with zero probability of error by a single use. Then the one-shot zero-error classical capacity equals to the…
Most general dynamics of an open quantum system is commonly represented by a quantum channel, which is a completely positive trace-preserving map (CPTP or Kraus map). Well-known are the representations of quantum channels by Choi matrices…
We completely determine the spectrum of an $I$-graph, that is, the eigenvalues of its adjacency matrix. We apply our result to prove known characterizations of connectedness and bipartiteness in $I$-graphs by using an spectral approach.…
We study a particular class of trace-preserving completely positive maps, called PQ-channels, for which classical and quantum evolutions are isolated in a certain sense. By combining open quantum random walks with a notion of recurrence, we…
For a quantum channel (completely positive, trace-preserving map), we prove a generalization to the infinite dimensional case of a result by Baumgartner and Narnhofer. This result is, in a probabilistic language, a decomposition of a…
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…
We obtain a classical analog of the quantum covariance matrix by performing its classical approximation for any continuous quantum state, and we illustrate this approach with the anharmonic oscillator. Using this classical covariance…
An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $\lambda_k$, $k=1,\ldots,n$, are distributed as follows $$ \lambda_1>-\lambda_2>\lambda_3>\cdots>(-1)^{n-1}\lambda_n>0. $$ A method for constructing sign…
We show that all scaling quantum graphs are explicitly integrable, i.e. any one of their spectral eigenvalues $E_n$ is computable analytically, explicitly, and individually for any given $n$. This is surprising, since quantum graphs are…
The explicit solution to the spectral problem of quantum graphs is used to obtain the exact distributions of several spectral statistics, such as the oscillations of the quantum momentum eigenvalues around the average, $\delta…
Comparison of statistical models (experiments) is an important branch of mathematical statistics, which gives deep insights in many aspects of foundation of statistics. So far, there are two quantum versions of the concept: Comparison with…
A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $\theta $, we find an explicit…
Time-reversibility measured by the deviation of the perturbed time-reversed motion from the unperturbed one is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrastive physical nature. Irrespective of…
We show that unbounded number of channel uses may be necessary for perfect transmission of quantum information. For any n we explicitly construct low-dimensional quantum channels ($d_A$=4, $d_E$=2 or 4) whose quantum zero-error capacity is…
We study classical and quantum maps on the torus phase space, in the presence of noise. We focus on the spectral properties of the noisy evolution operator, and prove that for any amount of noise, the quantum spectrum converges to the…