Related papers: Non-binary Entanglement-assisted Stabilizer Quantu…
Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the…
We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present…
The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this…
The entanglement spectrum (ES) provides a barometer of quantum entanglement and encodes physical information beyond that contained in the entanglement entropy. In this paper, we explore the ES of stabilizer codes, which furnish exactly…
Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
Proving the quantum Hamming bound for degenerate nonbinary stabilizer codes has been an open problem for a decade. In this note, I prove this bound for double error-correcting degenerate stabilizer codes. Also, I compute the maximum length…
This paper considers the use an entanglement breaking channel in the construction of a secure bit-commitment protocol. It is shown that this can be done via a depolarizing quantum channel.
In hybrid quantum systems a controllable coupling can be obtained by mediating the interactions with dynamically introduced photons. We propose a hybrid quantum architecture consisting of two nitrogen vacancy center ensembles coupled to a…
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…
Protecting information in systems that have more than two basis states (qudits) not only offers a promising route for reducing the number of individual quantum locations that must be protected, while more accurately reflecting the structure…
Quantum entanglement plays a crucial role in quantum computing. Entangling information has important implications for understanding the behavior of quantum programs and avoiding entanglement-induced errors. Entanglement analysis is a static…
Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its…
An algorithm for constructing Tanner graphs of non-binary irregular quasi-cyclic LDPC codes is introduced. It employs a new method for selection of edge labels allowing control over the code's non-binary ACE spectrum and resulting in low…
We investigate the dense coding in the case of non-symmetric Hilbert spaces of the sender and receiver's particles sharing the quantum maximally entangled state. The efficiency of classical information gain is also considered. We conclude…
We propose fault-tolerant encoders for quantum low-density parity check (LDPC) codes. By grouping qubits within a quantum code over contiguous blocks and applying preshared entanglement across these blocks, we show how transversal…
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to…
In this paper we propose a technique for distributing entanglement in architectures in which interactions between pairs of qubits are constrained to a fixed network $G$. This allows for two-qubit operations to be performed between qubits…