Related papers: An application of a matrix inequality in quantum i…
In this paper, we study the multiplicative behaviour of quantum channels, mathematically described by trace preserving, completely positive maps on matrix algebras. It turns out that the multiplicative domain of a unital quantum channel has…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the typical…
Quantum channels, pivotal in information processing, describe transformations within quantum systems and enable secure communication and error correction. Ergodic and mixing properties elucidate their behavior. In this paper, we establish a…
The information carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space,…
The well-known duality relating entangled states and noisy quantum channels is expressed in terms of a channel ket, a pure state on a suitable tripartite system, which functions as a pre-probability allowing the calculation of statistical…
Given two quantum channels, we examine the task of determining whether they are compatible - meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting…
A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum…
We give a survey of the two remarkable analytical problems of quantum information theory. The main part is a detailed report of the recent (partial) solution of the quantum Gaussian optimizers problem which establishes an optimal property…
In this note we discuss the geometry of matrix product states with periodic boundary conditions and provide three infinite sequences of examples where the quantum max-flow is strictly less than the quantum min-cut. In the first we fix the…
Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic…
Communication over a quantum channel that depends on a quantum state is considered when the encoder has channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. A full…
Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if…
We argue that notions in quantum theory should have universal properties in the sense of category theory. We consider the completely positive trace preserving (CPTP) maps, the basic notion of quantum channel. Physically, quantum channels…
Noisy quantum channels may be used in many information carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on…
We prove that for a large class of quantum Fisher information, a quantum channel is sufficient for a family of quantum states, i.e., the input states can be recovered from the output, if and only if the quantum Fisher information is…
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex,…
The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review,…
Quantum information theory is used to analize various non-linear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The…
Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…
We consider explicitly two examples of d-dimensional quantum channels with correlated noise and show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve…