Related papers: Unified and Generalized Approach to Entanglement-A…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
We explore how the quantum entanglement is modified in the generalized uncertainty principle (GUP)-corrected quantum mechanics by introducing the coupled harmonic oscillator system. Constructing the ground state $\rho_0$ and its reduced…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least…
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…
Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement…
Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the…
The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
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…
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…
Quantum information processing offers dramatic speedups, yet is famously susceptible to decoherence, the process whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
Quantum error correction (QEC) is essential for quantum computers to perform useful algorithms, but large-scale fault-tolerant computation remains out of reach due to demanding requirements on operation fidelity and the number of…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Traditionally, quantum entanglement has played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can exhibit results at odds with classical behavior. These…
The key realisation which lead to the emergence of the new field of quantum information processing is that quantum mechanics, the theory that describes microscopic particles, allows the processing of information in fundamentally new ways.…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…