Ultimate Limits for Quickest Quantum Change-Point Detection.

Detecting abrupt changes in data streams is crucial because they are often triggered by events that have important consequences if left unattended. Quickest change-point detection has become a vital sequential analysis primitive that aims at designing procedures that minimize the expected detection delay of a change subject to a bounded expected false alarm time. We put forward the quantum counterpart of this fundamental primitive on streams of quantum data. We give a lower bound on the mean minimum delay when the expected time of a false alarm is asymptotically large, under the most general quantum detection strategy, which is given by a sequence of adaptive collective (potentially weak) measurements on the growing string of quantum data. In addition, we give particular strategies based on repeated measurements on independent blocks of samples that asymptotically attain the lower bound and thereby establish the ultimate quantum limit for quickest change-point detection. Finally, we discuss online change-point detection in quantum channels.

Estimating Quantum and Private Capacities of Gaussian Channels via Degradable Extensions.

We present upper bounds on the quantum and private capacity of single-mode, phase-insensitive bosonic Gaussian channels based on degradable extensions. Our findings are state of the art in the following parameter regions: low temperature and high transmissivity for the thermal attenuator, low temperature for additive Gaussian noise, high temperature and intermediate amplification for the thermal amplifier.

Quantum Flags and New Bounds on the Quantum Capacity of the Depolarizing Channel.

A new upper bound for the quantum capacity of the d-dimensional depolarizing channels is presented. Our derivation makes use of a flagged extension of the map where the receiver obtains a copy of a state σ_{0} whenever the messages are transmitted without errors, and a copy of a state σ_{1}, when instead the original state gets fully depolarized. By varying the overlap between the flag states, the resulting transformation nicely interpolates between the depolarizing map (when σ_{0}=σ_{1}), and the d-dimensional erasure channel (when σ_{0} and σ_{1} have orthogonal support). We find sufficient conditions for degradability of the flagged channel, which let us calculate its quantum capacity in a suitable parameter region. From this last result we get the upper bound for the depolarizing channel, which by a direct comparison appears to be tighter than previous available results for d>2, and for d=2 it is tighter in an intermediate regime of noise. In particular, in the limit of large d values, our findings present a previously unnoticed O(1) correction.