Related papers: Error Correction by Structural Simplicity: Correct…
A family of high rate quantum error correcting codes adapted to the amplitude damping channel is presented. These codes are nonadditive and exploit self-complementarity structure to correct all first-order errors. Their rates can be higher…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
The zero-error channel capacity is the maximum asymptotic rate that can be reached with error probability exactly zero, instead of a vanishing error probability. The nature of this problem, essentially combinatorial rather than…
The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered…
We present a method for quantum error mitigation on partially error-corrected quantum computers - i.e., computers with some logical qubits and some noisy qubits. Our method is inspired by the error cancellation method and is implemented via…
We propose a new channel model for channels with synchronization errors. Using this model, we give simple, non-trivial and, in some cases, tight lower bounds on the capacity for certain synchronization error channels.
Motivated by mutation processes occurring in in-vivo DNA-storage applications, a channel that mutates stored strings by duplicating substrings as well as substituting symbols is studied. Two models of such a channel are considered: one in…
Zero-error coding encompasses a variety of source and channel problems where the probability of error must be exactly zero. This condition is stricter than that of the vanishing error regime, where the error probability goes to zero as the…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
Several communication models that are of relevance in practice are asymmetric in the way they act on the transmitted "objects". Examples include channels in which the amplitudes of the transmitted pulses can only be decreased, channels in…
Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…
The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword should tolerate $t$ asymmetric errors. Our main observation is…
Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code…
Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…
Systematic errors in quantum operations can be the dominating source of imperfection in achieving control over quantum systems. This problem, which has been well studied in nuclear magnetic resonance, can be addressed by replacing single…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…