Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0808.3851 · Physical Review A

Repeatable quantum memory channels

Tomáš Rybár, Mário Ziman

Published Nov 14, 2008• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.78.052114

Related papers

Quantum Channels with Memory

Tomáš Rybár

Abstract Quantum memory channels represent a very general, yet simple and comprehensible model for causal processes. As such they have attracted considerable research interest, mostly aimed on their transfer capabilities and structure properties. Most notably it was shown that memory channels can be implemented via physically naturally motivated collision models. We also define the concept of repeatable channels and show that only unital channels can be implemented repeatably with pure memory channels. In the special case of qubit channels we also show that every unital qubit channel has a repeatable implementation. We also briefly explore the possibilities of stroboscopical simulation of channels and show that all random unitary channels can be stroboscopically simulated. Particularly in qubit case, all indivisible qubit channels are also random unitary, hence for qubit all indivisible channels can be stroboscopically simulated. Memory channels also naturally capture the framework of correlated experiments. We develop methods to gather and interpret data obtained in such setting and in detail examine the two qubit case. We also show that for control unitary interactions the measured data will never contradict a simple unitary evolution. Thus no memory effects can be spotted then.

Acta Physica Slovaca Reviews and Tutorials•Nov 30, 2012•4 citations

Forgetfulness of continuous Markovian quantum channels

Cosmo Lupo, Laleh Memarzadeh, Stefano Mancini

The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.

arXiv:0907.1544•Physical Review A•Oct 27, 2009•15 citations

Quantifying the fidelity of a quantum memory

Victor Barizien, Sophie Egelhaaf, Angelo Gelmini Rodriguez +5 more

Quantum memories are key ingredients for future quantum networks. Developing methods for their certification is therefore an important, yet challenging, problem. In this work, we present a general framework for certifying quantum memories and quantifying their performance in an operational and efficient manner, taking advantage of developments in the theory of quantum channels. We start by giving a pedagogical introduction to these concepts and tools and illustrate their natural application to quantum memories. Specifically, we quantify the fidelity of a quantum memory via the notion of average channel fidelity, which can be estimated precisely in an experiment via a finite set of probe states forming a so-called $2$-design. We then present a number of witnessing techniques for certifying this quantity, and show that it gives access to other important properties of the channel, such as its dimensionality and its capacity to transmit quantum information. We consider mostly a simple prepare-and-measure scenario, but discuss also the case of an entanglement-based setup, as well as a semi-device-independent approach. Finally, we apply these methods to a solid-state quantum memory experiment, certifying an average channel fidelity of 98.6%. Our certification methods can be readily applied to other quantum devices, such as fibers, transducers and gates.

quant-pharXiv:2610.08445•Oct 7, 2026•0 citations

Quantum finite-depth memory channels: Case study

Tomáš Rybár, Mário Ziman

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.

Physical Review A•Oct 7, 2009•3 citations

Quantum Finite-Depth Memory Channels: Case Study

Mário Ziman, Tomáš Rybár

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.

arXiv:0907.5521•Jul 31, 2009•0 citations

Quantum channels and memory effects

Filippo Caruso, Vittorio Giovannetti, Cosmo Lupo +1 more

Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.

arXiv:1207.5435•Reviews of Modern Physics•Dec 10, 2014•329 citations
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.
Abstract Quantum memory channels represent a very general, yet simple and comprehensible model for causal processes. As such they have attracted considerable research interest, mostly aimed on their transfer capabilities and structure properties. Most notably it was shown that memory channels can be implemented via physically naturally motivated collision models. We also define the concept of repeatable channels and show that only unital channels can be implemented repeatably with pure memory channels. In the special case of qubit channels we also show that every unital qubit channel has a repeatable implementation. We also briefly explore the possibilities of stroboscopical simulation of channels and show that all random unitary channels can be stroboscopically simulated. Particularly in qubit case, all indivisible qubit channels are also random unitary, hence for qubit all indivisible channels can be stroboscopically simulated. Memory channels also naturally capture the framework of correlated experiments. We develop methods to gather and interpret data obtained in such setting and in detail examine the two qubit case. We also show that for control unitary interactions the measured data will never contradict a simple unitary evolution. Thus no memory effects can be spotted then.
The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.
Quantum memories are key ingredients for future quantum networks. Developing methods for their certification is therefore an important, yet challenging, problem. In this work, we present a general framework for certifying quantum memories and quantifying their performance in an operational and efficient manner, taking advantage of developments in the theory of quantum channels. We start by giving a pedagogical introduction to these concepts and tools and illustrate their natural application to quantum memories. Specifically, we quantify the fidelity of a quantum memory via the notion of average channel fidelity, which can be estimated precisely in an experiment via a finite set of probe states forming a so-called 222-design. We then present a number of witnessing techniques for certifying this quantity, and show that it gives access to other important properties of the channel, such as its dimensionality and its capacity to transmit quantum information. We consider mostly a simple prepare-and-measure scenario, but discuss also the case of an entanglement-based setup, as well as a semi-device-independent approach. Finally, we apply these methods to a solid-state quantum memory experiment, certifying an average channel fidelity of 98.6%. Our certification methods can be readily applied to other quantum devices, such as fibers, transducers and gates.
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.
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.
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.