144 research outputs found
Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
The set of doubly-stochastic quantum channels and its subset of mixtures of
unitaries are investigated. We provide a detailed analysis of their structure
together with computable criteria for the separation of the two sets. When
applied to O(d)-covariant channels this leads to a complete characterization
and reveals a remarkable feature: instances of channels which are not in the
convex hull of unitaries can return to it when either taking finitely many
copies of them or supplementing with a completely depolarizing channel. In
these scenarios this implies that a channel whose noise initially resists any
environment-assisted attempt of correction can become perfectly correctable.Comment: 31 page
Operational distance and fidelity for quantum channels
We define and study a fidelity criterion for quantum channels, which we term
the minimax fidelity, through a noncommutative generalization of maximal
Hellinger distance between two positive kernels in classical probability
theory. Like other known fidelities for quantum channels, the minimax fidelity
is well-defined for channels between finite-dimensional algebras, but it also
applies to a certain class of channels between infinite-dimensional algebras
(explicitly, those channels that possess an operator-valued Radon--Nikodym
density with respect to the trace in the sense of Belavkin--Staszewski) and
induces a metric on the set of quantum channels which is topologically
equivalent to the CB-norm distance between channels, precisely in the same way
as the Bures metric on the density operators associated with statistical states
of quantum-mechanical systems, derived from the well-known fidelity
(`generalized transition probability') of Uhlmann, is topologically equivalent
to the trace-norm distance.Comment: 26 pages, amsart.cls; improved intro, fixed typos, added a reference;
accepted by J. Math. Phy
Distinguishing classically indistinguishable states and channels
We investigate an original family of quantum distinguishability problems,
where the goal is to perfectly distinguish between quantum states that
become identical under a completely decohering map. Similarly, we study
distinguishability of quantum channels that cannot be distinguished when
one is restricted to decohered input and output states. The studied problems
arise naturally in the presence of a superselection rule, allow one to quantify
the amount of information that can be encoded in phase degrees of freedom
(coherences), and are related to time-energy uncertainty relation. We present a
collection of results on both necessary and sufficient conditions for the
existence of perfectly distinguishable states (channels) that are
classically indistinguishable.Comment: 22 pages, 8 figures. Published versio
Almost all quantum channels are equidistant
In this work we analyze properties of generic quantum channels in the case of
large system size. We use random matrix theory and free probability to show
that the distance between two independent random channels converges to a
constant value as the dimension of the system grows larger. As a measure of the
distance we use the diamond norm. In the case of a flat Hilbert-Schmidt
distribution on quantum channels, we obtain that the distance converges to
, giving also an estimate for the maximum success
probability for distinguishing the channels. We also consider the problem of
distinguishing two random unitary rotations.Comment: 30 pages, commets are welcom
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