Related papers: How Much Entanglement Does a Quantum Code Need?
We introduce a Steane-like enlargement procedure for entanglement-assisted quantum error-correcting codes (EAQECCs) obtained by considering Euclidean inner product. We give formulae for the parameters of these enlarged codes and apply our…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. However, because of the noise in quantum channels, it is difficult to distribute quantum entanglement over a long distance in…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
Entanglement detection is a fundamental task in quantum information science, serving as a cornerstone for quantum benchmarking and foundational studies. With an increasing qubit number that can be effectively controlled, there is a pressing…
The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure,…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
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.…
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…
Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a…
We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Entanglement is known to significantly improve the performance (separately) of communication and detection schemes that utilize quantum resources. This work explores the simultaneous utility of quantum entanglement for (joint) communication…
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…
In this paper, we investigate how to reduce the number of measurement configurations needed for sufficiently precise entanglement quantification. Instead of analytical formulae, we employ artificial neural networks to predict the amount of…
Quantum entanglement is a unique criterion of the quantum realm and an essential tool to secure quantum communication. Ensuring high-fidelity entanglement has always been a challenging task owing to interaction with the hostile channel…
We present a general framework of quantum error-correcting codes (QECCs) as a subspace of a complex Hilbert space and the corresponding error models. Then we illustrate how QECCs can be constructed using techniques from algebraic coding…