Generating random quantum channels

• URL: http://arxiv.org/abs/2011.02994v3
• Date: Wed, 19 May 2021 12:46:33 GMT
• Title: Generating random quantum channels
• Authors: Ryszard Kukulski, Ion Nechita, {\L}ukasz Pawela, Zbigniew Pucha{\l}a, Karol \.Zyczkowski
• Abstract summary: Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions they become mathematically equivalent. Additional results focus on the spectral gap and other spectral properties of random quantum channels and their invariant states.
• Score: 1.0499611180329802
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions they become mathematically equivalent, and lead to the uniform, Lebesgue measure on the convex set of quantum operations. We compare their advantages and computational complexity and demonstrate which of them is particularly suitable for numerical investigations. Additional results focus on the spectral gap and other spectral properties of random quantum channels and their invariant states. We compute mean values of several quantities characterizing a given quantum channel, including its unitarity, the average output purity and the $2$-norm coherence of a channel, averaged over the entire set of the quantum channels with respect to the uniform measure. An ensemble of classical stochastic matrices obtained due to super-decoherence of random quantum stochastic maps is analyzed and their spectral properties are studied using the Bloch representation of a classical probability vector.

Related papers

• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• 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)
• Upper bounds on probabilities in channel measurements on qubit channels and their applications [0.0]
  We derive the upper bounds of the probability in a channel measurement for specific classes of quantum channels. These applications demonstrate the significance of the obtained upper bounds.
  arXiv  Detail & Related papers  (2024-06-21T14:25:12Z)
• Random covariant quantum channels [2.9741863650371805]
  Group symmetries inherent in quantum channels often make them tractable. We introduce natural probability distributions for covariant quantum channels. We discuss the threshold phenomenon for positive partial transpose and entanglement breaking properties.
  arXiv  Detail & Related papers  (2024-03-06T12:39:30Z)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• Extreme quantum states and processes, and extreme points of general spectrahedra in finite dimensional algebras [0.27195102129094995]
  Convex sets of quantum states and processes play a central role in quantum theory and quantum information. Many important examples of convex sets in quantum theory are spectrahedra, that is, sets of positive operators subject to affine constraints. This contribution provides a characterisation of the extreme points of general spectrahedra, and bounds on the ranks of the corresponding operators.
  arXiv  Detail & Related papers  (2023-11-18T01:31:16Z)
• 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)
• Q-means using variational quantum feature embedding [0.9572675949441442]
  The objective of the Variational circuit is to maximally separate the clusters in the quantum feature Hilbert space. The output of the quantum circuit are characteristic cluster quantum states that represent a superposition of all quantum states belonging to a particular cluster. The gradient of the expectation value is used to optimize the parameters of the variational circuit to learn a better quantum feature map.
  arXiv  Detail & Related papers  (2021-12-11T13:00:51Z)
• Stochastic emulation of quantum algorithms [0.0]
  We introduce higher-order partial derivatives of a probability distribution of particle positions as a new object that shares basic properties of quantum mechanical states needed for a quantum algorithm. We prove that the propagation via the map built from those universal maps reproduces up to a prefactor exactly the evolution of the quantum mechanical state. We implement several well-known quantum algorithms, analyse the scaling of the needed number of realizations with the number of qubits, and highlight the role of destructive interference for the cost of emulation.
  arXiv  Detail & Related papers  (2021-09-16T07:54:31Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)

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.