On the eternal non-Markovianity of non-unital quantum channels
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909067932336128 |
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| author | Utagi, Shrikant Banerjee, Subhashish Srikanth, R. |
| author_facet | Utagi, Shrikant Banerjee, Subhashish Srikanth, R. |
| contents | The eternally non-Markovian Pauli channel is an example of a unital channel characterized by a negative decay rate for all time $t>0$. Here we consider the problem of constructing an analogous non-unital channel, and show in particular that a $d$-dimensional generalized amplitude damping (GAD) channel cannot be eternally non-Markovian when the non-Markovianity originates solely from the non-unital part of the channel. We study specific ramifications of this result for qubit GAD. Specifically, we construct a quasi-eternally non-Markovian qubit GAD channel, characterized by a time $t^\ast > 0$, such that the channel is non-Markovian only and for all time $t > t^\ast$. We further point out that our negative result for the qudit GAD channel, namely the impossibility of the eternal non-Markovian property, does not hold for a general qubit or higher-dimensional non-unital channel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_10625 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the eternal non-Markovianity of non-unital quantum channels Utagi, Shrikant Banerjee, Subhashish Srikanth, R. Quantum Physics Mathematical Physics The eternally non-Markovian Pauli channel is an example of a unital channel characterized by a negative decay rate for all time $t>0$. Here we consider the problem of constructing an analogous non-unital channel, and show in particular that a $d$-dimensional generalized amplitude damping (GAD) channel cannot be eternally non-Markovian when the non-Markovianity originates solely from the non-unital part of the channel. We study specific ramifications of this result for qubit GAD. Specifically, we construct a quasi-eternally non-Markovian qubit GAD channel, characterized by a time $t^\ast > 0$, such that the channel is non-Markovian only and for all time $t > t^\ast$. We further point out that our negative result for the qudit GAD channel, namely the impossibility of the eternal non-Markovian property, does not hold for a general qubit or higher-dimensional non-unital channel. |
| title | On the eternal non-Markovianity of non-unital quantum channels |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2203.10625 |