Cram\'er-Rao bound for time-continuous measurements in linear Gaussian quantum systems

We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve the numerical integration of a stochastic master equation for the corresponding density operator in a Hilbert space of infinite dimension, the formulas here derived depends only on the evolution of first and second moments of the quantum states, and thus can be easily evaluated without the need of any approximation. We also present some basic but physically meaningful examples where this result is exploited, calculating analytical and numerical bounds on the estimation of the squeezing parameter for a quantum parametric amplifier, and of a constant force acting on a mechanical oscillator in a standard optomechanical scenario.Comment: 9 pages, 2 figure

Optimal quantum repeaters for qubits and qudits

A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e. involve a single additional probe qubit, and optimal, i.e. provide the maximum information adding the minimum amount of noise. Information gain and state disturbance are quantified by fidelities which, for our schemes, saturate the ultimate bound imposed by quantum mechanics for randomly distributed signals. Special classes of signals are also investigated, in order to improve the information-disturbance trade-off. Extension to higher dimensional signals (qudits) is straightforward.Comment: Revised version. To appear in PR

A measure of the non-Gaussian character of a quantum state

We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in details the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single- and multi-mode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily computable for any state of a bosonic system and allows to define a corresponding measure for the non-Gaussian character of a quantum operation.Comment: revised and enlarged version, 7 pages, 4 figure

Continuous-variable entanglement distillation and non-commutative central limit theorems

Entanglement distillation transforms weakly entangled noisy states into highly entangled states, a primitive to be used in quantum repeater schemes and other protocols designed for quantum communication and key distribution. In this work, we present a comprehensive framework for continuous-variable entanglement distillation schemes that convert noisy non-Gaussian states into Gaussian ones in many iterations of the protocol. Instances of these protocols include (a) the recursive-Gaussifier protocol, (b) the temporally-reordered recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The flexibility of these protocols give rise to several beneficial trade-offs related to success probabilities or memory requirements, which that can be adjusted to reflect experimental demands. Despite these protocols involving measurements, we relate the convergence in this protocols to new instances of non-commutative central limit theorems, in a formalism that we lay out in great detail. Implications of the findings for quantum repeater schemes are discussed.Comment: published versio

Detecting Gaussian entanglement via extractable work

We show how the presence of entanglement in a bipartite Gaussian state can be detected by the amount of work extracted by a continuos variable Szilard-like device, where the bipartite state serves as the working medium of the engine. We provide an expression for the work extracted in such a process and specialize it to the case of Gaussian states. The extractable work provides a sufficient condition to witness entanglement in generic two-mode states, becoming also necessary for squeezed thermal states. We extend the protocol to tripartite Gaussian states, and show that the full structure of inseparability classes cannot be discriminated based on the extractable work. This suggests that bipartite entanglement is the fundamental resource underpinning work extraction.Comment: 12 pages, 8 figure

Non-equilibrium readiness and accuracy of Gaussian Quantum Thermometers

The dimensionality of a thermometer is key in the design of quantum thermometry schemes. In general, the phenomenology that is typical of finite-dimensional quantum thermometry does not apply to infinite dimensional ones. We analyse the dynamical and metrological features of non-equilibrium Gaussian Quantum Thermometers: on one hand, we highlight how quantum entanglement can enhance the readiness of composite Gaussian thermometers; on the other hand, we show that non-equilibrium conditions do not guarantee the best sensitivities in temperature estimation, thus suggesting the reassessment of the working principles of quantum thermometry