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Quantum operations, or quantum channels cannot be inverted in general. An arbitrary state passing through a quantum channel looses its fidelity with the input. Given a quantum channel ${cal E}$, we introduce the concept of its quasi-inverse as a map ${cal E}^{qi}$ which when composed with ${cal E}$ increases its average input-output fidelity in an optimal way. The channel ${cal E}^{qi}$ comes as close as possible to the inverse of a quantum channel. We give a complete classification of such maps for qubit channels and provide quite a few illustrative examples.
Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an operational inter
We show that any incoherent qubit channel could be decomposed into four incoherent Kraus operators. The proof consists in showing existence of four incoherent Kraus operators by decomposing the corresponding Choi-Jamiol{}kowski-Sudarshan matrix. We m
A complete analysis of multi-mode bosonic Gaussian channels is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a normal form. The maximum number of auxiliary modes
The states of three-qubit systems split into two inequivalent types of genuine tripartite entanglement, namely the Greenberger-Horne-Zeilinger (GHZ) type and the $W$ type. A state belonging to one of these classes can be stochastically transformed on