8 research outputs found
Information capacity of quantum observable
In this paper we consider the classical capacities of quantum-classical
channels corresponding to measurement of observables. Special attention is paid
to the case of continuous observables. We give the formulas for unassisted and
entanglement-assisted classical capacities and consider some
explicitly solvable cases which give simple examples of entanglement-breaking
channels with We also elaborate on the ensemble-observable duality
to show that for the measurement channel is related to the
-quantity for the dual ensemble in the same way as is related to the
accessible information. This provides both accessible information and the
-quantity for the quantum ensembles dual to our examples.Comment: 13 pages. New section and references are added concerning the
ensemble-observable dualit
Highly symmetric POVMs and their informational power
We discuss the dependence of the Shannon entropy of normalized finite rank-1
POVMs on the choice of the input state, looking for the states that minimize
this quantity. To distinguish the class of measurements where the problem can
be solved analytically, we introduce the notion of highly symmetric POVMs and
classify them in dimension two (for qubits). In this case we prove that the
entropy is minimal, and hence the relative entropy (informational power) is
maximal, if and only if the input state is orthogonal to one of the states
constituting a POVM. The method used in the proof, employing the Michel theory
of critical points for group action, the Hermite interpolation and the
structure of invariant polynomials for unitary-antiunitary groups, can also be
applied in higher dimensions and for other entropy-like functions. The links
between entropy minimization and entropic uncertainty relations, the Wehrl
entropy and the quantum dynamical entropy are described.Comment: 40 pages, 3 figure
Fundamental limits to quantum channel discrimination
What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we investigate the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations. In this general scenario, we first show how port-based teleportation can be used to simplify these adaptive protocols into a much simpler non-adaptive form, designing a new type of teleportation stretching. Then, we prove that the minimum error probability affecting the channel discrimination cannot beat a bound determined by the Choi matrices of the channels, establishing a general, yet computable formula for quantum hypothesis testing. As a consequence of this bound, we derive ultimate limits and no-go theorems for adaptive quantum illumination and single-photon quantum optical resolution. Finally, we show how the methodology can also be applied to other tasks, such as quantum metrology, quantum communication and secret key generation
Worst-case quantum hypothesis testing with separable measurements
10.22331/Q-2020-09-11-320Quantum