InĬomparison, the conditions in the point ( D ) represent a constraint † −closed algebra A, such that 1 l Y ∈ A. The latter, is aĬonstraint satisfaction problem with r 2 quadratic constrains S † E † j E i S ∝ 1 l X for the variable S ∈ M ( X, Y ), which Let usĬompare the point ( D ) with Knill-Laflamme conditions. The recovery subchannel is given as R = K ( ( α − 1 / 2 i i ′ A † i i ′ √ R ) i, i ′ ).įinally, the condition ( D ) gives us a simple method to check if E = K ( ( E i ) r i = 1 ) is probabilistically correctable for X. If the errors are caused by a unitary interaction with anĪuxiliary qubit system, we show that it is possible to restore a qubit logical Procedure for random noise channels, which is presented in
#Steinspring quantum error correction how to
Theorem 13 how to correct noise channels with bounded Choi Moreover, we discuss theĪdvantage of pQEC procedure over the deterministic one That to maximize the probability of successful error correction we need toĮncode the quantum information into a mixed state. We give anĮxplicit example of noise channels family (Section V), such We discover that optimal error-correcting codes are notĪlways generated with the usage of isometric encoding operations. (Theorem 1) to check, when probabilistic errorĬorrection is possible. Inspired by celebrated Knill-LaflammeĬonditions, we provide conditions Is lack of a formal description of its application for a general noise model. Learning unknown quantum operations or measurementĭespite the fact that pQEC procedure has been studied in the literature for a It is also worth mentioning, they were used with success in other fields of Potential to increase the spectrum of correctableĪre useful when the number of qubits is limited. ĭecoding operations have found application in stabilizerĮspecially for iterative probabilistic decoding in LDPCĬodes, error decoding or environment-assisted errorĬorrection. Output state and ask for a retransmission. Procedure may fail with some probability. This operation uses a classical postselection to determine if the encoded Physical bits, for example 0 → 000, 1 → 111. That to secure a one bit of information perfectly, it is necessary to use three Otherwise, if p > 2 3 it would be beneficial to use encoding 0 → 00ġ → 01 with the accepting states 10 and 11. We dismiss the cases 01 and 10 as they do not give conclusive answers. Information 00 at the decoding stage, we are certain the If we expect that p ≤ 2 3, then we can encode 0 → 00 and 1 → 11. ToĪ one bit of information, we use two physical bits. Consider the scenario, when the encodedĭata is harmed by a single bit error, that is with the probability p ∈ an arbitrary bit will be flipped. Procedure works, let us present an example of classical probabilisticĮrror correction. In this work, we study a particular QEC procedure called probabilistic
0 kommentar(er)
