Dephasing superchannels

• URL: http://arxiv.org/abs/2107.06585v2
• Date: Mon, 13 Dec 2021 15:51:34 GMT
• Title: Dephasing superchannels
• Authors: Zbigniew Pucha{\l}a, Kamil Korzekwa, Roberto Salazar, Pawe{\l} Horodecki, Karol \.Zyczkowski
• Abstract summary: We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel $mathcalE$. We prove that such superchannels $Xi_C$ form a particular subclass of Schur-product supermaps that act on the Jamiolkowski state $J(mathcalE)$ of a channel $mathcalE$ via a Schur product, $J'=J
• Score: 0.09545101073027092
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel $\mathcal{E}$, i.e., they leave invariant the transition probabilities induced by $\mathcal{E}$ in the distinguished basis. We prove that such superchannels $\Xi_C$ form a particular subclass of Schur-product supermaps that act on the Jamiolkowski state $J(\mathcal{E})$ of a channel $\mathcal{E}$ via a Schur product, $J'=J\circ C$. We also find physical realizations of general $\Xi_C$ through a pre- and post-processing employing dephasing channels with memory, and show that memory plays a non-trivial role for quantum systems of dimension $d>2$. Moreover, we prove that coherence generating power of a general quantum channel is a monotone under dephasing superchannels. Finally, we analyse the effect dephasing noise can have on a quantum channel $\mathcal{E}$ by investigating the number of distinguishable channels that $\mathcal{E}$ can be mapped to by a family of dephasing superchannels. More precisely, we upper bound this number in terms of hypothesis testing channel divergence between $\mathcal{E}$ and its fully dephased version, and also relate it to the robustness of coherence of $\mathcal{E}$.

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