Generating random quantum channels
Ryszard Kukulski,Ion Nechita,Łukasz Pawela,Zbigniew Puchała,Zbigniew Puchała,Karol Życzkowski,Karol Życzkowski +6 more
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TLDR
Three approaches to the problem of sampling of quantum channels are presented and it is shown under which conditions they become mathematically equivalent, and lead to the uniform, Lebesgue measure on the convex set of quantum operations.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.read more
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References
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I and i
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
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TL;DR: In this article, the basic aspects of entanglement including its characterization, detection, distillation, and quantification are discussed, and a basic role of entonglement in quantum communication within distant labs paradigm is discussed.
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On the Generators of Quantum Dynamical Semigroups
TL;DR: In this paper, the notion of a quantum dynamical semigroup is defined using the concept of a completely positive map and an explicit form of a bounded generator of such a semigroup onB(ℋ) is derived.
Book
The Theory of Open Quantum Systems
TL;DR: Probability in classical and quantum physics has been studied in this article, where classical probability theory and stochastic processes have been applied to quantum optical systems and non-Markovian dynamics in physical systems.