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 $\mathcal{E}$.

Related papers

• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Phase Transition in the Quantum Capacity of Quantum Channels [0.0]
  We prove that every quantum channel $Lambda$ in arbitrary dimension, when contaminated by white noise, completely loses its capacity of transmitting quantum states. We also find the quantum capacity of the complement of the depolarizing channel in closed form.
  arXiv  Detail & Related papers  (2024-08-11T09:49:52Z)
• General Communication Enhancement via the Quantum Switch [15.779145740528417]
  We conjecture that $mathcalP_n>0$ is both a necessary and sufficient condition for communication enhancement via the quantum $tt SWITCH$. We then formulate a communication protocol involving the quantum $tt SWITCH$ which enhances the private capacity of the BB84 channel.
  arXiv  Detail & Related papers  (2024-07-03T00:47:13Z)
• Capacities of a two-parameter family of noisy Werner-Holevo channels [0.0]
  In $d=2j+1$ dimensions, the Landau-Streater quantum channel is defined on the basis of spin $j$ representation of the $su(2)$ algebra. We extend this class of channels to higher dimensions in a way which is based on the Lie algebra $so(d)$ and $su(d)$.
  arXiv  Detail & Related papers  (2024-05-18T07:48:36Z)
• Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates [53.66705737169404]
  We consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Our main findings are that the maximum number of messages thus identifiable scales super-exponentially as $2R,nlog n$ with the block length $n$. Results are shown to generalise directly to classical-quantum channels with finite-dimensional output quantum system.
  arXiv  Detail & Related papers  (2024-02-14T11:59:30Z)
• Degradability of Modified Landau-Streater Type Low-Noise Quantum Channels in High Dimensions [10.720038857779135]
  We introduce and examine the Modified Landau-Streater (MLS) channels. These channels expand upon the qubit depolarizing and the recently proposed modified Werner-Holevo channels. Our results enhance the understanding of super-additivity in quantum channels within the low-noise regime.
  arXiv  Detail & Related papers  (2024-01-29T17:17:34Z)
• The quantum beam splitter with many partially indistinguishable photons: multiphotonic interference and asymptotic classical correspondence [44.99833362998488]
  We present the analysis of the quantum two-port interferometer in the $n rightarrow infty$ limit of $n$ partially indistinguishable photons. Our main result is that the output distribution is dominated by the $O(sqrtn)$ channels around a certain $j*$ that depends on the degree of indistinguishability. The form is essentially the doubly-humped semi-classical envelope of the distribution that would arise from $2 j*$ indistinguishable photons, and which reproduces the corresponding classical intensity distribution.
  arXiv  Detail & Related papers  (2023-12-28T01:48:26Z)
• Weyl channels for multipartite systems [42.37986459997699]
  Quantum channels describe unitary and non-unitary evolution of quantum systems. We show that these channels are completely characterized by elements drawn of finite cyclic groups.
  arXiv  Detail & Related papers  (2023-10-17T02:45:47Z)
• Majorization ladder in bosonic Gaussian channels [0.0]
  We show that the channel output resulting from the $ntextth$ energy eigenstate (Fock state) majorizes the channel output resulting from the $(n!+!1)textth$ energy eigenstate (Fock state) This reflects a remarkable link between the energy at the input of the channel and a disorder relation at its output as captured by majorization theory.
  arXiv  Detail & Related papers  (2022-09-17T18:19:26Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Bosonic quantum communication across arbitrarily high loss channels [68.58838842613457]
  A general attenuator $Phi_lambda, sigma$ is a bosonic quantum channel that acts by combining the input with a fixed environment state. We show that for any arbitrary value of $lambda>0$ there exists a suitable single-mode state $sigma(lambda)$. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity.
  arXiv  Detail & Related papers  (2020-03-19T16:50:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.