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We address parameter estimation for complex/structured systems and suggest an effective estimation scheme based on continuous-variables quantum probes. In particular, we investigate the use of a single bosonic mode as a probe for Ohmic reservoirs, and obtain the ultimate quantum limits to the precise estimation of their cutoff frequency. We assume the probe prepared in a Gaussian state and determine the optimal working regime, i.e. the conditions for the maximization of the quantum Fisher information in terms of the initial preparation, the reservoir temperature and the interaction time. Upon investigating the Fisher information of feasible measurements we arrive at a remarkable simple result: homodyne detection of canonical variables allows one to achieve the ultimate quantum limit to precision under suitable, mild, conditions. Finally, upon exploiting a perturbative approach, we find the invariant sweet spots of the (tunable) characteristic frequency of the probe, able to drive the probe towards the optimal working regime.
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Quantum illumination is the task of determining the presence of an object in a noisy environment. We determine the optimal continuous variable states for quantum illumination in the limit of zero object reflectivity. We prove that the optimal single mode state is a coherent state, while the optimal two mode state is the two-mode squeezed-vacuum state. We find that these probes are not optimal at non-zero reflectivity, but remain near optimal. This demonstrates the viability of the continuous variable platform for an experimentally accessible, near optimal quantum illumination implementation.
We propose a procedure for tomographic characterization of continuous variable quantum operations which employs homodyne detection and single-mode squeezed probe states with a fixed degree of squeezing and anti-squeezing and a variable displacement and orientation of squeezing ellipse. Density matrix elements of a quantum process matrix in Fock basis can be estimated by averaging well behaved pattern functions over the homodyne data. We show that this approach can be straightforwardly extended to characterization of quantum measurement devices. The probe states can be mixed, which makes the proposed procedure feasible with current technology.
With the rise of quantum technologies, it is necessary to have practical and preferably non-destructive methods to measure and read-out from such devices. A current line of research towards this has focussed on the use of ancilla systems which couple to the system under investigation, and through their interaction, enable properties of the primary system to be imprinted onto and inferred from the ancillae. We propose the use of continuous variable qumodes as ancillary probes, and show that the interaction Hamiltonian can be fully characterised and directly sampled from measurements of the qumode alone. We suggest how such probes may also be used to determine thermodynamical properties, including reconstruction of the partition function. We show that the method is robust to realistic experimental imperfections such as finite-sized measurement bins and squeezing, and discuss how such probes are already feasible with current experimental setups.
It is often the case that the environment of a quantum system may be described as a bath of oscillators with Ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence or to tailor quantum information protocols. Recently, the use of quantum probes in characterizing Ohmic environments at zero-temperature has been discussed, showing that a single qubit provides precise estimation of the cutoff frequency. On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to complex system at thermal equilibrium. In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision {attainable by} quantum probes. Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e. values of the order $omega_c lesssim T$ (in natural units). For larger values of $omega_c$ decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure.
We study two continuous variable systems (or two harmonic oscillators) and investigate their entanglement evolution under the influence of non-Markovian thermal environments. The continuous variable systems could be two modes of electromagnetic fields or two nanomechanical oscillators in the quantum domain. We use quantum open system method to derive the non-Markovian master equations of the reduced density matrix for two different but related models of the continuous variable systems. The two models both consist of two interacting harmonic oscillators. In model A, each of the two oscillators is coupled to its own independent thermal reservoir, while in model B the two oscillators are coupled to a common reservoir. To quantify the degrees of entanglement for the bipartite continuous variable systems in Gaussian states, logarithmic negativity is used. We find that the dynamics of the quantum entanglement is sensitive to the initial states, the oscillator-oscillator interaction, the oscillator-environment interaction and the coupling to a common bath or to different, independent baths.
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