Quantum Information Transmission over a Partially Degradable Channel

We investigate a quantum coding for quantum communication over a PD (partially degradable) degradable quantum channel. For a PD channel, the degraded environment state can be expressed from the channel output state up to a degrading map. PD channels can be restricted to the set of optical channels which allows for the parties to exploit the benefits in experimental quantum communications. We show that for a PD channel, the partial degradability property leads to higher quantum data rates in comparison to those of a degradable channel. The PD property is particular convenient for quantum communications and allows one to implement the experimental quantum protocols with higher performance. We define a coding scheme for PD-channels and give the achievable rates of quantum communication.Comment: 7 pages, 2 figures, Journal-ref: IEEE Acces

Quantum channels and their entropic characteristics

One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite dimensional quantum systems. We also touch upon the "continuous-variables" case, which provides an arena for quantum Gaussian systems. Most of the practical realizations of quantum information processing were implemented in such systems, in particular based on principles of quantum optics. Several important entropic quantities are introduced and used to describe the basic channel capacity formulas. The remarkable role of the specific quantum correlations - entanglement - as a novel communication resource, is stressed.Comment: review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys. (in press

Quantum Channel Capacities with Passive Environment Assistance

We initiate the study of passive environment-assisted communication via a quantum channel, modeled as a unitary interaction between the information carrying system and an environment. In this model, the environment is controlled by a benevolent helper who can set its initial state such as to assist sender and receiver of the communication link. (The case of a malicious environment, also known as jammer, or arbitrarily varying channel, is essentially well-understood and comprehensively reviewed.) Here, after setting out precise definitions, focussing on the problem of quantum communication, we show that entanglement plays a crucial role in this problem: indeed, the assisted capacity where the helper is restricted to product states between channel uses is different from the one with unrestricted helper. Furthermore, prior shared entanglement between the helper and the receiver makes a difference, too.Comment: 14 pages, 13 figures, IEEE format, Theorem 9 (statement and proof) changed, updated References and Example 11 added. Comments are welcome

The structure of degradable quantum channels

Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or anti-degradable and present a complete description of anti-degradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions ($d_B$ and $d_E$ respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with a environment that is "small" in the sense $d_E \leq d_B$. Perhaps surprisingly, we also present examples of degradable channels with ``large'' environments, in the sense that the minimal dimension $d_E > d_B$. Indeed, one can have $d_E > \tfrac{1}{4} d_B^2$. In the case of channels with diagonal Kraus operators, we describe the subclass which are complements of entanglement breaking channels. We also obtain a number of results for channels in the convex hull of conjugations with generalized Pauli matrices. However, a number of open questions remain about these channels and the more general case of random unitary channels.Comment: 42 pages, 3 figures, Web and paper abstract differ; (v2 contains only minor typo corrections

The Private Classical Capacity of a Partially Degradable Quantum Channel

For a partially degradable (PD) channel, the channel output state can be used to simulate the degraded environment state. The quantum capacity of a PD channel has been proven to be additive. Here, we show that the private classical capacity of arbitrary dimensional PD channels is equal to the quantum capacity of the channel and also single-letterizes. We prove that higher rates of private classical communication can be achieved over a PD channel in comparison to standard degradable channels.Comment: 10 pages, Journal-ref: Physica Scripta, Special Issue on Quantum Information (2014

The Structure and Quantum Capacity of a Partially Degradable Quantum Channel

The quantum capacity of degradable quantum channels has been proven to be additive. On the other hand, there is no general rule for the behavior of quantum capacity for non-degradable quantum channels. We introduce the set of partially degradable (PD) quantum channels to answer the question of additivity of quantum capacity for a well-separable subset of non-degradable channels. A quantum channel is partially degradable if the channel output can be used to simulate the degraded environment state. PD channels could exist both in the degradable, non-degradable and conjugate degradable family. We define the term partial simulation, which is a clear benefit that arises from the structure of the complementary channel of a PD channel. We prove that the quantum capacity of an arbitrary dimensional PD channel is additive. We also demonstrate that better quantum data rates can be achieved over a PD channel in comparison to standard (non-PD) channels. Our results indicate that the partial degradability property can be exploited and yet still hold many benefits for quantum communications.Comment: 59 pages, 13 figures, Journal-ref: IEEE Acces