Related papers: Correcting Quantum Errors with Entanglement
Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
Quantum error correction assisted by entanglement helps to transmit the encoded qudits through quantum channels with some of them being noiseless. Here we consider a more realistic scheme for experiments what we called as partial-noisy…
We introduce the notion of entanglement of subspaces as a measure that quantify the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block…
Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code,…
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…
We study the effects of quantum entanglement on the performance of two classical zero-error communication tasks among multiple parties. Both tasks are generalizations of the two-party zero-error channel-coding problem, where a sender and a…
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
We consider the problem of coding for quantum channels with side information that is available ahead of time at the transmitter but not at the receiver. We find a single-letter expression for the entanglement-assisted quantum capacity of…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known…
Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the…
Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a…
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,…
Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the non-local operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
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…