We also give a proof on a generalization of binary Singleton type bound on entanglement-assisted quantum error-correcting codes to arbitrary q-ary entanglement-assisted quantum error-correcting codes. Numerical examples in modest lengths show that our constructions perform better than known constructions in the literature. The main ideas include linear complementary dual codes and related concatenation constructions. We also give a proof on a generalization of binary Singleton type bound on entanglement-assisted quantum error-correcting codes to arbitrary q-ary entanglement-assisted quantum error-correcting codes.ĪB - We present two new constructions of entanglement-assisted quantum error-correcting codes using some fundamental properties of (classical) linear codes in an effective way. N2 - We present two new constructions of entanglement-assisted quantum error-correcting codes using some fundamental properties of (classical) linear codes in an effective way. We study the operator algebra quantum error correction in the GNS Hilbert space which applies to any quantum system including the local algebra of quantum. We give an explicit example of noise channels. N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. that optimal error-correcting codes are not always generated with the usage of isometric encoding operations. In the past two decades, various constructions of quantum error-correcting codes (QECCs. ![]() ![]() It follows that the boundary to the bulk map is a Petz map.T1 - New constructions of entanglement-assisted quantum codes Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. Here we tackle this challenge by introducing a graphically intuitive quantum lego framework for both analyzing and constructing quantum error correction codes. In gauge/gravity dualities, the bulk relative entropy of holographic states is the same as their boundary relative entropies which implies that the holographic map is an error correction code, and hence a conditional expectation. Similar to the RG, the composition of the error map followed by the recovery map forms a conditional expectation (a projection in the GNS Hilbert space). We show that the recovery map is an isometric embedding of the correctable subalgebra. We study the operator algebra quantum error correction in the GNS Hilbert space which applies to any quantum system including the local algebra of quantum field theory. We demonstrate that a set of states are preserved under this map if and only if their pairwise relative entropies do not change when we restrict to the long-distance observables. We show that if there is a state that is preserved under renormalization the coarse-graining step is the Petz dual of the isometric embedding (the Petz map). The coarse-graining is the error map and the long-distance observables are the correctable operators. Furthermore it is an isometry for the Hamming metric. It is comprised of a coarse-graining step followed by an isometric embedding. A q-ary quantum error-correcting code of length n and dimension. That is the day when a robust quantum computer, like this one, will be able to crack the most common encryption method used to secure our digital data. Here, we study the compatibility of these two important principles. We show that the real-space renormalization group (RG), as a map from the observable algebra to the subalgebra of long-distance observables, is an error correction code, best described by a conditional expectation. Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. In many applications, including quantum communication and quantum error correction, it is useful to encode a quantum state of one system into a quantum. To this end, the quantum information is encoded into a larger system in such a way that any effect of the noise on the data can be undone.
0 Comments
Leave a Reply. |