42 research outputs found
Informationally complete sets of Gaussian measurements
We prove necessary and sufficient conditions for the informational
completeness of an arbitrary set of Gaussian observables on continuous variable
systems with finite number of degrees of freedom. In particular, we show that
an informationally complete set either contains a single informationally
complete observable, or includes infinitely many observables. We show that for
a single informationally complete observable, the minimal outcome space is the
phase space, and the observable can always be obtained from the quantum optical
-function by linear postprocessing and Gaussian convolution, in a suitable
symplectic coordinatization of the phase space. In the case of projection
valued Gaussian observables, e.g., generalized field quadratures, we show that
an informationally complete set of observables is necessarily infinite.
Finally, we generalize the treatment to the case where the measurement coupling
is given by a general linear bosonic channel, and characterize informational
completeness for an arbitrary set of the associated observables.Comment: 10 pages, 2 figure
Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection
The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator.
The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively.
In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.Siirretty Doriast
Measuring position and moment together
We describe an operational scheme for determining both the position and
momentum distributions in a large class of quantum states, together with an
experimental implementation.Comment: 4 pages, no figures, to be published in Phys. Lett.
Quantum resource control for noisy Einstein-Podolsky-Rosen steering with qubit measurements
We demonstrate how quantum optimal control can be used to enhance quantum
resources for bipartite one-way protocols, specifically EPR-steering with qubit
measurements. Steering is relevant for one-sided device-independent key
distribution, the realistic implementations of which necessitate the study of
noisy scenarios. So far mainly the case of imperfect detection efficiency has
been considered; here we look at the effect of dynamical noise responsible for
decoherence and dissipation. In order to set up the optimisation, we map the
steering problem into the equivalent joint measurability problem, and employ
quantum resource-theoretic robustness monotones from that context. The
advantage is that incompatibility (hence steerability) with arbitrary pairs of
noisy qubit measurements has been completely characterised through an
analytical expression, which can be turned into a computable cost function with
exact gradient. Furthermore, dynamical loss of incompatibility has recently
been illustrated using these monotones. We demonstrate resource control
numerically using a special gradient-based software, showing, in particular,
the advantage over naive control with cost function chosen as a fidelity in
relation to a specific target. We subsequently illustrate the complexity of the
control landscapes with a simplified two-variable scheme. The results
contribute to the theoretical understanding of the limitations in realistic
implementations of quantum information protocols, also paving way to practical
use of the rather abstract quantum resource theories.Comment: updated figures and minor text modifications in v
Remote parameter estimation in a quantum spin chain enhanced by local control
We study the interplay of control and parameter estimation on a quantum spin
chain. A single qubit probe is attached to one end of the chain, while we wish
to estimate a parameter on the other end. We find that control on the probe
qubit can substantially improve the estimation performance and discover some
interesting connections to quantum state transfer.Comment: 7 pages, 3 figure