Quantum coherence is a fundamental aspect of quantum physics and plays a central role in quantum information science. This essential property of the quantum states could be fragile under the influence of the quantum operations. The extent to which quantum coherence is diminished depends both on the channel and the incoherent basis. Motivated by this, we propose a measure of nonclassicality of a quantum channel as the average quantum coherence of the state space after the channel acts on, minimized over all orthonormal basis sets of the state space. Utilizing the squared l1-norm of coherence for the qubit channels, the minimization can be treated analytically and the proposed measure takes a closed form of expression. If we allow the channels to act locally on a maximally entangled state, the quantum correlation is diminished making the states more classical. We show that the extent to which quantum correlation is preserved under local action of the channel cannot exceed the quantumness of the underlying channel. We further apply our measure to the quantum teleportation protocol and show that a nonzero quantumness for the underlying channel provides a necessary condition to overcome the best classical protocols. arXiv:1808.00754v2 [quant-ph]
We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the previous results of Karimipour et al (2020 Phys. Rev. A 101 032109) to arbitrary dimensional channels and to the classical domain. We demonstrate how application of the proposed scheme can increase on the average the fidelity between a given random pure state and its image transformed by the quantum channel followed by its quasi-inversion.
We analyze the set ANQ of mixed unitary channels represented in the Weyl basis and accessible by a Lindblad semigroup acting on an N-level quantum system. General necessary and sufficient conditions for a mixed Weyl quantum channel of an arbitrary dimension to be accessible by a semigroup are established. The set ANQ is shown to be log-convex and star-shaped with respect to the completely depolarizing channel. A decoherence supermap acting in the space of Lindblad operators transforms them into the space of Kolmogorov generators of classical semigroups. We show that for mixed Weyl channels, the super-decoherence commutes with the dynamics so that decohering a quantum accessible channel, we obtain a bistochastic matrix from the set ANC of classical maps accessible by a semigroup. Focusing on three-level systems, we investigate the geometry of the sets of quantum accessible maps, its classical counterpart, and the support of their spectra. We demonstrate that the set A3Q is not included in the set U3Q of quantum unistochastic channels, although an analogous relation holds for N = 2. The set of transition matrices obtained by super-decoherence of unistochastic channels of order N ≥ 3 is shown to be larger than the set of unistochastic matrices of this order and yields a motivation to introduce the larger sets of k-unistochastic matrices.
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