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Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance for…
We investigate effective noise channels for encoded quantum systems with and without active error correction. Noise acting on physical qubits forming a logical qubit is thereby described as a logical noise channel acting on the logical…
Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to…
We define C*-algebras on a Fock space such that the Hamiltonians of quantum field models with positive mass are affiliated to them. We describe the quotient of such algebras with respect to the ideal of compact operators and deduce…
Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…
We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved,…
This paper considers the comparison of noisy channels from the viewpoint of statistical decision theory. Various orderings are discussed, all formalizing the idea that one channel is "better" than another for information transmission. The…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of…
In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the…
Coherence is a basic notion for quantum states. Instead of quantum states, in this work, We establish a resource theory for quantifying the coherence of Gaussian channels. To do this, we propose the definitions of incoherent Gaussian…
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…
Quantum transport on structured networks is strongly influenced by interference effects, which can dramatically modify how information propagates through a system. We develop a quantum-information-theoretic framework for scattering on…
The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…
For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
Sender and receiver can control noisy channels by means of the resources they own, that is local operations, potentially correlated using classical communication, and entangled pairs shared between them. Using the Choi-Jamiolkowski…
Quantum computing hardware is affected by quantum noise that undermine the quality of results of an executed quantum program. Amongst other quantum noises, coherent error that caused by parameter drifting and miscalibration, remains…
Coherent errors, and especially those that occur in correlation among a set of qubits, are detrimental for large-scale quantum computing. Correlations in noise can occur as a result of spatial and temporal configurations of instructions…