Abstract Lossy bosonic channels play an important role in a number of quantum information tasks, since they well approximate thermal dissipation in an experiment. Here, we characterize their metrological power in the idler-free and entanglement-assisted cases, using respectively single- and two-mode Gaussian states as probes. In the problem of estimating the loss parameter, we study the power-constrained quantum Fisher information (QFI) for generic temperature and loss parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum state optimizes the QFI for any value of the loss parameter and temperature. We discuss the optimization of the total QFI, where the number of probes is allowed to vary by keeping the total power constrained. In this context, we elucidate the role of the ‘shadow-effect’, or passive signature, for reaching a quantum advantage. Finally, we discuss the implications of our results for the quantum illumination and quantum reading protocols.
Abstract Lossy bosonic channels play an important role in a number of quantum information tasks, since they well approximate thermal dissipation in an experiment. Here, we characterize their metrological power in the idler-free and entanglement-assisted cases, using respectively single- and two-mode Gaussian states as probes. In the problem of estimating the loss parameter, we study the power-constrained quantum Fisher information (QFI) for generic temperature and loss parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum state optimizes the QFI for any value of the loss parameter and temperature. We discuss the optimization of the total QFI, where the number of probes is allowed to vary by keeping the total power constrained. In this context, we elucidate the role of the ‘shadow-effect’, or passive signature, for reaching a quantum advantage. Finally, we discuss the implications of our results for the quantum illumination and quantum reading protocols.
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 Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is well-characterized under full channel knowledge, we address the inverse problem, namely, the precise estimation of fundamental channel parameters, including the beam splitter transmissivity and the two-mode squeezing amplitude. Employing the quantum Fisher information (QFI) as a benchmark for metrological sensitivity, we demonstrate that the symmetry inherent in mode mixing critically governs the amplification of QFI, thereby enabling high-precision parameter estimation. In addition, we investigate quantum thermometry by estimating the average photon number of thermal states, revealing that the transmissivity parameter significantly modulates estimation precision. Our results underscore the metrological utility of two-mode Gaussian states and establish a robust framework for parameter inference in noisy and dynamically evolving quantum systems.
We study the maximum quantum Fisher information (QFI) for estimating a single parameter embedded in a generic multimode lossless passive Gaussian unitary using general Gaussian probes under a signal-energy constraint. Unlike previous work, which imposed a total energy constraint on the full probe, we constrain only the transmitted signal modes while allowing an arbitrary number of locally retained ancilla modes with arbitrarily large energy. We prove that this additional freedom does not increase the maximum achievable QFI; the optimum remains identical to that attainable without extra ancilla energy. The same conclusion also extends to the sequential setting under a total energy constraint. We also characterize the family of optimal probe states and show that entanglement is not necessary to attain the optimum in the lossless setting. This extends the result of Matsubara et al. to the physically motivated signal-energy-constrained scenario and establishes a no-go theorem for ancilla-assisted Gaussian enhancement in noiseless passive-unitary estimation.
We obtain universal (i.e., probe and measurement-independent) performance bounds on ancilla-assisted quantum sensing of multiple parameters of phase-covariant optical channels under energy and mode-number constraints. We first show that for any such constrained problem, an optimal ancilla-entangled probe can always be found whose reduced state on the modes probing the channel is diagonal in the photon-number basis. For parameters that are encoded in single-mode Gaussian channels, we derive a universal upper bound on the quantum Fisher information matrix that delineates the roles played by the energy and mode constraints. We illustrate our results for sensing of the transmittance of a thermal loss channel under both the no-passive-signature and passive-signature paradigms, and in the problem of sensing the noise variance of an additive-noise channel. In both cases, we show that two-mode squeezed vacuum probes are near-optimal under the constraints in the regime of low signal brightness, i.e., per-mode average photon number. More generally, our work sets down a uniform framework for readily evaluating universal limits for any sensing problem involving Gaussian channels.
Gaussian quantum states and channels are pivotal across many branches of quantum science and their applications, including the processing and storage of quantum information, the investigation of thermodynamics in the quantum regime, and quantum computation. The great advantage is that Gaussian states are experimentally accessible via their first and second statistical moments. In this work, we investigate parameter estimation for Gaussian states, in which the probe-state preparation stage involves two noncommutative Gaussian measurements on the position and momentum observables, introducing tunable parameters. The influence of these noncommutative Gaussian measurements is investigated through the quantum Fisher information (QFI). We showed that the QFI for characterizing Gaussian channels can be increased by adjusting the uncertainty parameters in the preparation of the probe state. Furthermore, if the probe is initially in a thermal state, probe-state preparation may generate quantum coherence in its energy basis. We showed that not only does the amount of coherence affect the improvement of the QFI, but also the rate of change of the coherence with respect to the parameter to be estimated. The proposed probe-state protocol is applied to two paradigmatic single-mode Gaussian channels, the attenuator and amplification channels, which are building blocks of Gaussian quantum information. Our results contribute to the use of coherence in quantum metrology and are experimentally feasible in quantum-optical devices.
We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form of compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within d-dimensional cutoff subspaces ($d\ensuremath{\leqslant}6$) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.