Related papers: Approximate quantum error correction, covariance s…
Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…
We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
It is shown that, if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for…
The essence of quantum error-correction is to use redundant Hilbert space to identify and correct errors, and the channel fidelity of the quantum channel does not affect which errors can be identified and corrected. Based on this, it is…
The concept of entropy and the correct application of the Second Law of thermodynamics are essential in order to understand the reason why quantum error correction is thermodynamically possible and no violation of the Second Law occurs…
The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…
It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies…
We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs…
Quantum metrology stands as a leading application of quantum science and technology, yet noise often constrains its precision and sensitivity. In near-term quantum metrology, existing protocols largely depend on virtual state purification,…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
We introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle"…
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we…
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…
We introduce measures of quantum coherence as the speed of evolution of a system under decoherence. That is, coherence is the ability to estimate a dephasing channel, quantified by the quantum Fisher information. We extend the analysis to…
We make an explicit connection between fundamental notions in quantum cryptography and quantum error correction. Error-correcting subsystems (and subspaces) for quantum channels are the key vehicles for contending with noise in physical…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum…
The precise and automated calibration of quantum gates is a key requirement for building a reliable quantum computer. Unlike errors from decoherence, systematic errors can in principle be completely removed by tuning experimental…
We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is…