Quantum Memory Channels Research Articles

Quantum finite-depth memory channels: Case study

We analyze the depth of the memory of quantum memory channels generated by a fixed unitary transformation describing the interaction between the principal system and internal degrees of freedom of the process device. We investigate the simplest case of a qubit memory channel with a two-level memory system. In particular, we explicitly characterize all interactions for which the memory depth is finite. We show that the memory effects are either infinite, or they disappear after at most two uses of the channel. Memory channels of finite depth can be to some extent controlled and manipulated by so-called reset sequences. We show that actions separated by the sequences of inputs of the length of the memory depth are independent and constitute memoryless channels.

Theoretical framework for quantum networks

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination, estimation, and tomography. Our framework is based on the concepts of quantum comb---which describes all transformations achievable by a given quantum network---and link product---the operation of connecting two quantum networks. Quantum networks are treated both from a constructive point of view---based on connections of elementary circuits---and from an axiomatic one---based on a hierarchy of admissible quantum maps. In the axiomatic context a fundamental property is shown, which we call universality of quantum memory channels: any admissible transformation of quantum networks can be realized by a suitable sequence of memory channels. The open problem whether this property fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.

Enhancement of Transmission Rates in Quantum Memory Channels with Damping

We consider the transfer of quantum information down a single-mode quantum transmission line. Such a quantum channel is modeled as a damped harmonic oscillator, the interaction between the information carriers -a train of N qubits- and the oscillator being of the Jaynes-Cummings kind. Memory effects appear if the state of the oscillator is not reset after each channel use. We show that the setup without resetting is convenient in order to increase the transmission rates, both for the transfer of quantum and classical private information. Our results can be applied to the micromaser.

Repeatable quantum memory channels

Within the framework of quantum memory channels we introduce the notion of repeatability of quantum channels. In particular, a quantum channel is called repeatable if there exists a memory device implementing the same channel on each individual input. We show that random unitary channels can be implemented in a repeatable fashion, whereas the nonunital channels cannot.

Models for Quantum Memory Channels

We discuss a couple of models aimed to describe memory effects in quantum channels. We start from a rather intuitive model and arrive to a more abstract one which turns out to be more general.

Quantum channels with memory

We present a general model for quantum channels with memory and show that it is sufficiently general to encompass all causal automata: any quantum process in which outputs up to some time $t$ do not depend on inputs at times ${t}^{\ensuremath{'}}>t$ can be decomposed into a concatenated memory channel. We then examine and present different physical setups in which channels with memory may be operated for the transfer of (private) classical and quantum information. These include setups in which either the receiver or a malicious third party have control of the initializing memory. We introduce classical and quantum channel capacities for these settings and give several examples to show that they may or may not coincide. Entropic upper bounds on the various channel capacities are given. For forgetful quantum channels, in which the effect of the initializing memory dies out as time increases, coding theorems are presented to show that these bounds may be saturated. Forgetful quantum channels are shown to be open and dense in the set of quantum memory channels.

A dynamical model for quantum memory channels

A dynamical model for quantum channel is introduced which allows one to pass continuously from the memoryless case to the case in which memory effects are present. The quantum and classical communication rates of the model are defined and explicit expression are provided in some limiting case. In this context we introduce noise attenuation strategies where part of the signals are sacrificed to modify the channel environment. The case of qubit channel with phase damping noise is analyzed in details.

Bounds on classical information capacities for a class of quantum memory channels

The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real world communication channels experience noise which is modelled better by errors that are correlated between separate channel uses. In this paper, upper bounds on the classical information capacities of a class of quantum memory channels are derived. The class of channels consists of indecomposable quantum memory channels, a generalization of classical indecomposable finite-state channels.