14,008 research outputs found
Coherifying quantum channels
Is it always possible to explain random stochastic transitions between states
of a finite-dimensional system as arising from the deterministic quantum
evolution of the system? If not, then what is the minimal amount of randomness
required by quantum theory to explain a given stochastic process? Here, we
address this problem by studying possible coherifications of a quantum channel
, i.e., we look for channels that induce the same
classical transitions , but are "more coherent". To quantify the coherence
of a channel we measure the coherence of the corresponding
Jamio{\l}kowski state . We show that the classical transition matrix
can be coherified to reversible unitary dynamics if and only if is
unistochastic. Otherwise the Jamio{\l}kowski state of
the optimally coherified channel is mixed, and the dynamics must necessarily be
irreversible. To assess the extent to which an optimal process
is indeterministic we find explicit bounds on the entropy
and purity of , and relate the latter to the unitarity of
. We also find optimal coherifications for several classes
of channels, including all one-qubit channels. Finally, we provide a
non-optimal coherification procedure that works for an arbitrary channel
and reduces its rank (the minimal number of required Kraus operators) from
to .Comment: 20 pages, 8 figures. Published versio
Direct Characterization of Quantum Dynamics: General Theory
The characterization of the dynamics of quantum systems is a task of both
fundamental and practical importance. A general class of methods which have
been developed in quantum information theory to accomplish this task is known
as quantum process tomography (QPT). In an earlier paper [M. Mohseni and D. A.
Lidar, Phys. Rev. Lett. 97, 170501 (2006)] we presented a new algorithm for
Direct Characterization of Quantum Dynamics (DCQD) of two-level quantum
systems. Here we provide a generalization by developing a theory for direct and
complete characterization of the dynamics of arbitrary quantum systems. In
contrast to other QPT schemes, DCQD relies on quantum error-detection
techniques and does not require any quantum state tomography. We demonstrate
that for the full characterization of the dynamics of n d-level quantum systems
(with d a power of a prime), the minimal number of required experimental
configurations is reduced quadratically from d^{4n} in separable QPT schemes to
d^{2n} in DCQD.Comment: 17 pages, 6 figures, minor modifications are mad
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