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The essence of quantum error-correction is to use redundant Hilbert space to identify and correct errors, and the channel fidelity of the quantum channel does not affect which errors can be identified and corrected. Based on this, it is…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum…
We introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle"…
We study error correction type protocols in which a quantum channel encodes logical information into an enlarged Hilbert space. Specifically, we consider channels realized by one dimensional random noisy quantum circuits with spatially…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum…
We show that private shared reference frames can be used to perform private quantum and private classical communication over a public quantum channel. Such frames constitute a novel type of private shared correlation (distinct from private…
We present a protocol for quantum cryptography in which the data obtained for mismatched bases are used in full for the purpose of quantum state tomography. Eavesdropping on the quantum channel is seriously impeded by requiring that the…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
Is there a meaningful quantum counterpart to public communication? We argue that the symmetric-side channel -- which distributes quantum information symmetrically between the receiver and the environment -- is a good candidate for a notion…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
This paper investigates properties of noisy quantum information channels. We define a new quantity called {\em coherent information} which measures the amount of quantum information conveyed in the noisy channel. This quantity can never be…
We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We…
Quantum channels represent a broad spectrum of operations crucial to quantum information theory, encompassing everything from the transmission of quantum information to the manipulation of various resources. In the domain of states, the…