相关论文: The equivalence between correctability of deletion…
This paper shows that Knill-Laflamme condition, known as a necessary and sufficient condition for quantum error-correction, can be applied to quantum errors where the number of particles changes before and after the error. This fact shows…
Quantum synchronisation errors are a class of quantum errors that change the number of qubits in a quantum system. The classical error correction of synchronisation errors has been well-studied, including an insertion-deletion equivalence…
This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
A simple and unifying method to show the perfect error-correcting condition is provided based on the quantum mutual information. The one-to-one parameterization of quantum operations and the properties of the quantum relative entropy are…
We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad.…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
We investigate the most general notion of a private quantum code, which involves the encoding of qubits into quantum subsystems and subspaces. We contribute to the structure theory for private quantum codes by deriving testable conditions…
This manuscript presents a construction method for quantum codes capable of correcting multiple deletion errors. By introducing two new alogorithms, the alternating sandwich mapping and the block error locator, the proposed method reduces…
This manuscript is an extended abstract version of the paper entitled ``Quantum Deletion Codes derived from Classical Deletion Codes.'' The paper contributes to the fundamental theory for quantum deletion error-correcting codes. The paper…
We study the approximate correctability of general algebras of observables, which represent hybrid quantum-classical information. This includes approximate quantum error correcting codes and subsystems codes. We show that the main result of…
Quantum deletions, which are harder to correct than erasure errors, occur in many realistic settings. It is therefore pertinent to develop quantum coding schemes for quantum deletion channels. To date, not much is known about which explicit…
We introduce an intrinsic formulation of quantum error correction based on representation theory, in which error-protection structure is encoded directly in a unitary group representation, rather than being tied to a particular embedding…
We consider the problem of correcting insertion and deletion errors in the $d$-dimensional space. This problem is well understood for vectors (one-dimensional space) and was recently studied for arrays (two-dimensional space). For vectors…
In conventional quantum mechanics, quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned, respectively. Here, we investigate the quantum…
In this paper, we assume an error such that a single insertion occurs and then a single deletion occurs. Under such an error model, this paper provides a decoding algorithm for non-binary quantum codes constructed by Matsumoto and Hagiwara.
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…
We demonstrate that quantum error correction is realized by the renormalization group in scalar field theories. We construct $q$-level states by using coherent states in the IR region. By acting on them the inverse of the unitary operator…