Quantum ranging is crucial in several applications such as radar and localization. This paper determines the quantum advantage of ranging with single-mode displaced squeezed states. Exact analytical expressions for the quantum Fisher information (QFI) about the range parameter are derived in the presence of thermal loss channels characterized by arbitrary loss and noise parameters. The quantum advantage, termed as gain, is determined as a ratio of QFI with and without employing squeezing. It is shown that the gain can be unboundedly large in the optical regime whereas it is upper bounded in the microwave regime.
Quantum ranging is crucial in several applications such as radar and localization. This paper determines the quantum advantage of ranging with single-mode displaced squeezed states. Exact analytical expressions for the quantum Fisher information (QFI) about the range parameter are derived in the presence of thermal loss channels characterized by arbitrary loss and noise parameters. The quantum advantage, termed as gain, is determined as a ratio of QFI with and without employing squeezing. It is shown that the gain can be unboundedly large in the optical regime whereas it is upper bounded in the microwave regime.
The ability to determine distances from dedicated measurements, namely active ranging, is crucial in a variety of systems including localization, radar, and lidar. This thesis establishes the quantum limits and determines the quantum advantage provided by single-beam displaced squeezed states in active ranging. Analytical expressions of the quantum Fisher information (QFI) are provided for monochromatic and continuous-mode waves passing through a thermal loss channel with arbitrary loss and noise conditions. The optimal allocation of system resources for performing displacement and squeezing operations is determined. The optimal allocation consists of apportioning all resources to perform either the displacement operation, providing no quantum advantage, or the squeezing operation. Analytical results are examined in optical and microwave regimes. The optimal gain, i.e., the ratio between the QFI obtained by optimal resource allocation and the QFI obtained by performing only the displacement operation, is derived for the optical and microwave regimes. Quantum advantage afforded by the prototypical heterodyne receiver is also investigated. The results of this thesis pave the way for establishing a foundation of active ranging and provide insights for system design employing currently available quantum technologies.
We investigate quantum advantages in loss sensing when the two-mode squeezed vacuum state is used as a probe. Following an experimental demonstration in PRX 4, 011049, we consider a quantum scheme in which the signal mode is passed through the target and a thermal noise is introduced to the idler mode before they are measured. We consider two detection strategies of practical relevance: coincidence-counting and intensity-difference measurement, which are widely used in quantum sensing and imaging experiments. By computing the signal-to-noise ratio, we verify that quantum advantages persist even under strong thermal background noise, in comparison with the classical scheme which uses a single-mode coherent state that directly suffers from the thermal noise. Such robustness comes from the fact that the signal mode suffers from the thermal noise in the classical scheme, while in the quantum scheme, the idler mode does. For a fairer comparison, we further investigate a different setup in which the thermal noise is introduced to the signal mode in the quantum schemes. In this new setup, we show that the quantum advantages are significantly reduced. Remarkably, however, under an optimum measurement scheme associated with the quantum Fisher information, we show that the two-mode squeezed vacuum state does exhibit a quantum advantage over the entire range of the environmental noise and loss. We expect this work to serve as a guide for experimental demonstrations of quantum advantages in loss parameter sensing, which is subject to lossy and noisy environment.
A paradigmatic task in quantum metrology is that of phase estimation. For this task it is commonly believed, under reasonable assumptions about prior information, that a quadratic advantage in sensitivity is the maximum possible advantage offered by the use of quantum resources. In this work, we consider a channel that implements a phase shift by an angle 2πk/M, where k is a uniformly random unknown integer, in addition to a small unknown phase shift of interest. We show that, subject to a constraint on the mean photon number per channel use, there is a super-exponential separation between the quantum Fisher information (QFI) attainable using a squeezed vacuum state and that attainable using coherent states. This advantage holds over any state obtained from a coherent state via phase covariant channels. Specifically, when the mean photon number per channel use is 1, the ratio of their QFI grows as Ω[(M/2e)M]. For a mean photon number per channel use of M/log(M), the squeezed vacuum QFI is Ω(M3/2/log(M)), whereas for a coherent state it is at most exp[−Mloglog(M)+O(M)]. We complement this QFI analysis with non-asymptotic estimation results. For a mean photon number per channel use of M/logM, an explicit squeezed-vacuum protocol estimates the phase to accuracy O(1/M) using O(MlogM) channel uses, whereas every coherent state protocol requires at least exp[MloglogM−O(M)] channel uses. We consider the effects of noise and show that the ratio of their QFIs can still grow super-exponentially in M. Finally, under fixed optical loss and thermal noise, choosing nˉ=M2/(logM)3/2 allows squeezed vacuum with heterodyne detection to achieve accuracy O(1/M) using sub-polynomially many channel uses, whereas every protocol in the specified classical family requires super-polynomially many.
A Doppler radar is a device that employs the Doppler effect to estimate the radial velocity of a moving target at a distance. Traditional radars are based on a classical description of the electromagnetic radiation, but in principle their performance can be improved employing entangled quantum probe states. For target detection, i.e. hypothesis testing, a quantum advantage exists even in the high-noise regime appropriate to describe microwave fields, a protocol known as quantum illumination. In this paper, we show a similar advantage also for a quantum Doppler radar operating in presence of thermal noise, whereas so far a quantum advantage was shown in the noiseless scenario or in lidars operating at optical frequencies with negligible thermal noise. Concretely, we quantify the radar performance in terms of the quantum Fisher information, which captures the ultimate precision allowed by quantum mechanics in the asymptotic regime. We compare a classical protocol based on coherent states with a quantum one that uses multimode states obtained from spontaneous parametric downconversion. To ensure a fair comparison we match the signal energy and pulse duration. We show that a 3dB advantage is possible in the regime of small number of signal photons and high thermal noise, even for low transmissivity.
Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well known, provided that the quantum channels are completely characterized. In this work, we have studied the role played by quantum coherence in the estimation of Gaussian channel parameters. For this purpose, we start by considering an initial single-mode vacuum state where coherence is generated through displaced or/and squeezing operations. Then, we consider a probe state with two resources, the average thermal number and the quantum coherence. The results are computed using the quantum Fisher information (QFI) as well as some gain functions defined in the work. We applied the estimation protocol for two paradigmatic bosonic Gaussian channels: the thermal attenuator and the thermal amplifier. Our results show that for the vacuum initial state, coherence can be exploited to obtain a high QFI. Moreover, we can state two important facts: the first being that for a small parameter region of a channel, the QFI depends on the mechanism used to generate the coherence, while the second is that the QFI depends not only on the amount of coherence but also on how it changes as a function of the parameter to be estimated. For the probe state, including also an average thermal number, the two examples show that thermal resources are not always beneficial to the QFI and that this depends on the channel structure. For the attenuator channel, the optimal probe state is only limited by the ability to implement an average thermal number and generate an amount of coherence, while for the amplifier channel, the vacuum probe state with coherence is the optimal state. Finally, we obtain a direct relation between the quantum Fisher information and the relative entropy of coherence, allowing, in principle, an experimental verification based on the measurement of the covariance matrix of the probe system.
Abstract In this work, we theoretically investigate single-mode Gaussian quantum coherence from a comprehensive perspective. Based on analytical expressions of the first and second moments of single-mode Gaussian states undergoing various Gaussian noisy channels, we use quantum mater equation and the method of the relative entropy to quantify the quantum coherence of any single-mode Gaussian state. We demonstrate that the displaced thermal state achieves maximum quantum coherence when using only the displaced vacuum state, which is a pure coherent state. However, for various lossy noise channels, quantum coherence shows a significant decrease. In the context of a squeezed thermal state, when controlling the squeezing parameter for a given environmental temperature, quantum coherence has been witnessed to increase. The ultimate upper bound of quantum coherence is then attained with the squeezed vacuum state. In particular, we determined the most generalized scenario of the displaced squeezed thermal state. The maximum value of quantum coherence is obtained when displacement and squeeze parameters both attain maximum value. Our study might be important in the future for the characterisation as well as the estimation of various nonclassical quantum correlations in single-mode Gaussian states.