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arXiv:1811.07589 · Physical Review A

Engineering fidelity of the generalized Pauli channels via legitimate memory kernels

Katarzyna Siudzińska, Dariusz Chruściński

Published Jul 8, 2019• 11 citations
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Abstract

We analyze the fidelity of the generalized Pauli channels governed by memory kernel master equations. It is shown that by appropriate engineering of parameters of the corresponding memory kernel, the quantum evolution with nonlocal noise can have higher fidelity than the corresponding purely Markovian evolution governed by the Markovian semigroup. Similar engineering can substantially influence the evolution of quantum entanglement, entropy, and quantum coherence. Interestingly, by adding a nonlocal noise, one can protect the system against a sudden death of entanglement.

DOI
10.1103/physreva.100.012303

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We analyze the fidelity of the generalized Pauli channels governed by memory kernel master equations. It is shown that by appropriate engineering of parameters of the corresponding memory kernel, the quantum evolution with nonlocal noise can have higher fidelity than the corresponding purely Markovian evolution governed by the Markovian semigroup. Similar engineering can substantially influence the evolution of quantum entanglement, entropy, and quantum coherence. Interestingly, by adding a nonlocal noise, one can protect the system against a sudden death of entanglement.
In this paper we analyze the evolution of generalized Pauli channels governed by the memory kernel master equation. We provide necessary and sufficient conditions for the memory kernel to give rise to legitimate (completely positive and trace-preserving) quantum evolution. In particular, we analyze a class of kernels generating the quantum semi-Markov evolution, which is a natural generalization of the Markovian semigroup. Interestingly, the convex combination of Markovian semigroups goes beyond the semi-Markov case. Our analysis is illustrated with several examples.
We derive sufficient conditions for the memory-kernel governing nonlocal master equation which guarantee a legitimate (completely positive and trace-preserving) dynamical map. It turns out that these conditions provide natural parametrizations of the dynamical map being a generalization of the Markovian semigroup. This parametrization is defined by the so-called legitimate pair---monotonic quantum operation and completely positive map---and it is shown that such a class of maps covers almost all known examples from the Markovian semigroup, the semi-Markov evolution, up to collision models and their generalization.
It is by now well established that noise itself can be useful for performing quantum information processing tasks. We present results which show how one can effectively reduce the error rate associated with a noisy quantum channel by counteracting its detrimental effects with another form of noise. In particular, we consider the effect of adding on top of a purely Markovian (Lindblad) dynamics, a more general form of dissipation, which we refer to as generalized-Markovian noise. This noise has an associated memory kernel and the resulting dynamics are described by an integrodifferential equation. The overall dynamics are characterized by decay rates which depend not only on the original dissipative time scales but also on the new integral kernel. We find that one can engineer this kernel such that the overall rate of decay is lowered by the addition of this noise term. We illustrate this technique for the case where the bare noise is described by a dephasing Pauli channel. We analytically solve this model and show that one can effectively double (or even triple) the length of the channel, while achieving the same fidelity, entanglement, and error threshold. We numerically verify this scheme can also be used to protect against thermal Markovian noise (at nonzero temperature), which models spontaneous emission and excitation processes. A physical interpretation of this scheme is discussed, whereby the added generalized-Markovian noise causes the system to become periodically decoupled from the background Markovian noise.