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- W3197387573 abstract "Modeling open quantum systems is a difficult task for many experiments. A standard method for modeling open system evolution uses an environment that is initially uncorrelated with the system in question, evolves the two unitarily, and then traces over the bath degrees of freedom to find an effective evolution of the system. This model can be insufficient for physical systems that have initial correlations. Specifically, there are evolutions (rho _S=text {tr}_E(rho _{SE})rightarrow rho _S'=text {tr}_E(Urho _{SE}U^dagger )) which cannot be modeled as (rho _S=text {tr}_E(rho _{SE})rightarrow rho _S'=text {tr}_E(Urho _Sotimes rho _E U^dagger )). An example of this is (rho _{SE}= left| {varPhi ^+} rightrangle leftlangle {varPhi ^+} right| ) and (U_{SE}=text {CNOT}) with control on the environment. Unfortunately, there is no known method of modeling an open quantum system which is completely general. We first present some restrictions on the availability of completely positive (CP) maps via the standard prescription. We then discuss some implications a more general treatment would have for quantum control methods. In particular, we provide a theorem that restricts the reversibility of a map that is not completely positive (NCP). Let (varPhi ) be NCP and (tilde{varPhi }) be the corresponding CP map given by taking the absolute value of the coefficients in (varPhi ). The theorem shows that the CP reversibility conditions for (tilde{varPhi }) do not provide reversibility conditions for (varPhi ) unless (varPhi ) is positive on the domain of the code space." @default.
- W3197387573 created "2021-09-13" @default.
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- W3197387573 date "2021-01-01" @default.
- W3197387573 modified "2023-09-27" @default.
- W3197387573 title "Error Correction for Correlated Quantum Systems" @default.
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- W3197387573 doi "https://doi.org/10.1007/978-3-030-63591-6_34" @default.
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