scholarly journals Encoding classical information in gauge subsystems of quantum codes

2022 ◽  
Author(s):  
Andrew Nemec ◽  
Andreas Klappenecker
Keyword(s):  
Quantum Information ◽  
Linear Codes ◽  
Explicit Construction ◽  
Quantum Codes ◽  
Classical Information ◽  
Hybrid Code ◽  
Gauge Fixing ◽  
Minimum Distances

In this paper, we show how to construct hybrid quantum-classical codes from subsystem codes by encoding the classical information into the gauge qudits using gauge fixing. Unlike previous work on hybrid codes, we allow for two separate minimum distances, one for the quantum information and one for the classical information. We give an explicit construction of hybrid codes from two classical linear codes using Bacon–Casaccino subsystem codes, as well as several new examples of good hybrid code.

Quantum codes from nearly self-orthogonal quaternary linear codes

2014 ◽  
Vol 73 (2) ◽  
pp. 417-424 ◽  
Author(s):  
Petr Lisoněk ◽  
Vijaykumar Singh
Keyword(s):  
Linear Codes ◽  
Quantum Codes ◽  
Quaternary Linear Codes

Entanglement-assisted quantum codes achieving the quantum singleton bound but violating the quantum hamming bound

2014 ◽  
Vol 14 (13&14) ◽  
pp. 1107-1116
Author(s):  
Ruihu Li ◽  
Luobin Guo ◽  
Zongben Xu
Keyword(s):  
Error Correction ◽  
Infinite Family ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Singleton Bound ◽  
Minimum Distances ◽  
Quantum Error

We give an infinite family of degenerate entanglement-assisted quantum error-correcting codes (EAQECCs) which violate the EA-quantum Hamming bound for non-degenerate EAQECCs and achieve the EA-quantum Singleton bound, thereby proving that the EA-quantum Hamming bound does not asymptotically hold for degenerate EAQECCs. Unlike the previously known quantum error-correcting codes that violate the quantum Hamming bound by exploiting maximally entangled pairs of qubits, our codes do not require local unitary operations on the entangled auxiliary qubits during encoding. The degenerate EAQECCs we present are constructed from classical error-correcting codes with poor minimum distances, which implies that, unlike the majority of known EAQECCs with large minimum distances, our EAQECCs take more advantage of degeneracy and rely less on the error correction capabilities of classical codes.

Probabilistic secret sharing through noise quantum channe

2012 ◽  
Vol 12 (3&4) ◽  
pp. 253-261
Author(s):  
Satyabrata Adhikari ◽  
Indranil Chakrabarty ◽  
Pankaj Agrawal
Keyword(s):  
Quantum Information ◽  
Secret Sharing ◽  
Mixed State ◽  
Pure State ◽  
Noisy Channel ◽  
Noisy Channels ◽  
Superdense Coding ◽  
Classical Information ◽  
Phase Damping ◽  
Realistic Situation

In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.

A class of quaternary linear codes improving known minimum distances

2014 ◽  
Vol 78 (3) ◽  
pp. 615-627 ◽  
Author(s):  
Martin Steinbach ◽  
Dirk Hachenberger
Keyword(s):  
Linear Codes ◽  
Minimum Distances ◽  
Quaternary Linear Codes

scholarly journals Binary construction of quantum codes of minimum distances five and six

2008 ◽  
Vol 308 (9) ◽  
pp. 1603-1611 ◽  
Author(s):  
Ruihu Li ◽  
Xueliang Li
Keyword(s):  
Quantum Codes ◽  
Minimum Distances

scholarly journals The Information Coding in the Time Structure of the Object of a Laser Pulse in an Optical Echo Processor

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
L. A. Nefediev ◽  
A. R. Sakhbieva
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Laser Pulses ◽  
Information Coding ◽  
Algorithmic Information Theory ◽  
Time Intervals ◽  
Classical Information ◽  
Information Transformation ◽  
Algorithmic Information ◽  
Echo Processor

The encoding of information in time intervals of an echelon of laser pulses of an object pulse in the optical echo processor is considered. The measures of information are introduced to describe the transformation of classical information in quantum information. It is shown that in the description of information transformation into quantum information, the most appropriate measure is a measure of quantum information based on the algorithmic information theory.

scholarly journals Encryption with weakly random keys using quantum ciphertext

2012 ◽  
Vol 12 (5&6) ◽  
pp. 395-403
Author(s):  
Jan Bouda ◽  
Matej Pivoluska ◽  
Martin Plesch
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Single Case ◽  
Full Information ◽  
Classical Information ◽  
Random Source ◽  
Random Keys

The lack of perfect randomness can cause significant problems in securing communication between two parties. McInnes and Pinkas \cite{McInnesPinkas-ImpossibilityofPrivate-1991} proved that unconditionally secure encryption is impossible when the key is sampled from a weak random source. The adversary can always gain some information about the plaintext, regardless of the cryptosystem design. Most notably, the adversary can obtain full information about the plaintext if he has access to just two bits of information about the source (irrespective on length of the key). In this paper we show that for every weak random source there is a cryptosystem with a classical plaintext, a classical key, and a quantum ciphertext that bounds the adversary's probability $p$ to guess correctly the plaintext strictly under the McInnes-Pinkas bound, except for a single case, where it coincides with the bound. In addition, regardless of the source of randomness, the adversary's probability $p$ is strictly smaller than $1$ as long as there is some uncertainty in the key (Shannon/min-entropy is non-zero). These results are another demonstration that quantum information processing can solve cryptographic tasks with strictly higher security than classical information processing.

scholarly journals Both classical & quantum information: both bit & qubit. Both physical & transcendental time

2021 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Information ◽  
Mathematical Concept ◽  
Classical Information ◽  
Finite Series ◽  
Physical Action ◽  
Time Arrow

Information can be considered as the most fundamental, philosophical,physical and mathematical concept originating from the totality by means of physicaland mathematical transcendentalism (the counterpart of philosophicaltranscendentalism). Classical and quantum information, particularly by their units, bitand qubit, correspond and unify the finite and infinite. As classical information isrelevant to finite series and sets, as quantum information, to infinite ones. Afundamental joint relativity of the finite and infinite, of the external and internal is tobe investigated. The corresponding invariance is able to define physical action and itsquantity only on the basis of information and especially: on the relativity of classicaland quantum information. The concept of transcendental time, an epoché in relation tothe direction of time arrow can be defined. Its correlate is that information invariant tothe finite and infinite, therefore unifying both classical and quantum information.

New quantum codes from two linear codes

2020 ◽  
Vol 19 (3) ◽  
Author(s):  
Xiusheng Liu ◽  
Peng Hu
Keyword(s):  
Linear Codes ◽  
Quantum Codes
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