Abstract In bosonic quantum metrology, the estimate of a loss parameter is typically performed by means of pure states, such as coherent, squeezed or entangled states, while mixed thermal probes are discarded for their inferior performance. Here we show that thermal sources with suitable correlations can be engineered in such a way to approach, or even surpass, the error scaling of coherent states in the presence of general Gaussian decoherence. This decoherence is modeled by including bosonic loss, thermal noise, and even the possibility of environmental correlations, so as to simulate non-Markovian dynamics. Our findings pave the way for practical quantum metrology with thermal sources in optical instruments (e.g., photometers) or at different wavelengths (e.g., far infrared, microwave or x-ray) where the generation of quantum features, such as coherence, squeezing or entanglement, may be extremely challenging.
Abstract In bosonic quantum metrology, the estimate of a loss parameter is typically performed by means of pure states, such as coherent, squeezed or entangled states, while mixed thermal probes are discarded for their inferior performance. Here we show that thermal sources with suitable correlations can be engineered in such a way to approach, or even surpass, the error scaling of coherent states in the presence of general Gaussian decoherence. This decoherence is modeled by including bosonic loss, thermal noise, and even the possibility of environmental correlations, so as to simulate non-Markovian dynamics. Our findings pave the way for practical quantum metrology with thermal sources in optical instruments (e.g., photometers) or at different wavelengths (e.g., far infrared, microwave or x-ray) where the generation of quantum features, such as coherence, squeezing or entanglement, may be extremely challenging.
In bosonic quantum metrology, the estimate of a loss parameter is typically performed by means of pure states, such as coherent, squeezed or entangled states, while mixed thermal probes are discarded for their inferior performance. Here we show that thermal sources with suitable correlations can be engineered in such a way to approach, or even surpass, the error scaling of coherent states in the presence of general Gaussian decoherence. Our findings pave the way for practical quantum metrology with thermal sources in optical instruments (e.g., photometers) or at different wavelengths (e.g., far infrared, microwave or X-ray) where the generation of quantum features, such as coherence, number states, squeezing or entanglement, may be extremely challenging.
The major problem of multiparameter quantum estimation theory is to find an ultimate measurement scheme to go beyond the standard quantum limits that each quasi-classical estimation measurement is limited by. Although, in some specifics quantum protocols without environmental noise, the ultimate sensitivity of a multiparameter quantum estimation can beat the standard quantum limit. However, the presence of noise imposes limitations on the enhancement of precision due to the inevitable existence of environmental fluctuations. Here, we address the motivation behind the usage of Gaussian quantum resources and their advantages in reaching the standard quantum limits under realistic noise. In this context, our work aims to explore the ultimate limits of precision for the simultaneous estimation of a pair of parameters that characterize the displacement channel acting on Gaussian probes and subjected to open dynamics. More precisely, we focus on a general two-mode mixed squeezed displaced thermal state, after reducing it to various Gaussian probes states, like; a two-mode pure squeezed vacuum, two-mode pure displaced vacuum, two-mode mixed displaced thermal, two-mode mixed squeezed thermal. To study the ultimate estimation precision, we evaluate the upper and bottom bound of HCRB in various cases. We find that when the entangled states, two-mode pure squeezed vacuum and two-mode mixed squeezed thermal, are employed as probes states, the upper and bottom bound of HCRB beats the standard quantum limit in the presence of a noisy environment.
Abstract We study the estimation precision attainable by entanglement-enhanced Ramsey interferometry in the presence of spatiotemporally correlated non-classical noise. Our analysis relies on an exact expression of the reduced density matrix of the qubit probes under general zero-mean Gaussian stationary dephasing, which is established through cumulant-expansion techniques and may be of independent interest in the context of non-Markovian open dynamics. By continuing and expanding our previous work (Beaudoin et al 2018 Phys. Rev. A 98 020102(R)), we analyze the effects of a non-collective coupling regime between the qubit probes and their environment, focusing on two limiting scenarios where the couplings may take only two or a continuum of possible values. In the paradigmatic case of spin–boson dephasing noise from a thermal environment, we find that it is in principle possible to suppress, on average, the effect of spatial correlations by randomizing the location of the probes, as long as enough configurations are sampled where noise correlations are negative. As a result, superclassical precision scaling is asymptotically restored for initial entangled states, including experimentally accessible one-axis spin-squeezed states.
We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.
In this thesis I study optimal strategies to estimate or characterize quantum states and processes (quantum channels). I consider the problem of estimating a phase encoded on a gaussian state. Phase estimation is at the heart of many quantum metrology applications, such as gravitational wave detectors or clock synchronization. I address the problem to the phase estimation fidelity for pure and mixed gaussian states and study how temperature affects the precision of estimation. Although the case of pure states has been studied before, very little is known about estimation in mixed states. The interest in mixed gaussian states relies on the fact that these are the states one has in real experiments with light due to the unavoidable presence of noise. Displaced and squeezed thermal states are studied. For the case of displaced states, I find that fidelity estimation gets worse when the temperature increases. On the contrary, for squeezed thermal states I find the surprising result that a larger temperature yields better estimation. This apparently paradoxical feature, also appears when I derive the estimation accuracy that can be obtained when an asymptotically large number of copies of the state is available. I also study quantum benchmarks that can be applied to a wide variety of protocols, such us quantum storage or quantum teleportation. A very important question in QIT is to know whether a particular quantum protocol can be realized by classical means with the same efficiency. After all, QIT lives from the promise of this quantum advantage. This question becomes specially relevant in experimental (real) implementations of quantum schemes. In real experiments there are always losses and the ideal quantum protocols become imperfect. It is then necessary to assess whether the same experimental result could be obtained by classical (less costly) means. So, for example, in a particular teleportation experiment -which involves generation of entanglement, complicated Bell measurements, fighting decoherence, etc.- one might ask whether one could achieve the same (i.e. mapping the state of a system to a second system located in a different place or time) by measuring the system, transmitting the collected information to the other location, and finally preparing the system accordingly. It is hence of paramount importance to give bounds on the efficiency of these measure and prepare (or entanglement breaking) channels. For this purpose we propose a threshold based on a phase-covariant family of states. Besides of being a family with a straightforward group-theoretical structure, which gives obvious computational advantages, this family is interesting because it can be tested experimentally also in a straightforward way. A crucial feature for the practical use of our benchmark is that it does not require pure (ideal) input states. I finally consider the problem of estimating the parameter of the amplification channel. The amplification channel is interesting by itself but also by the fact that the Hawking-Unruh effect can be formally modeled by it. The Unruh-Hawking effect is a relativistic effect and as such it is hard to measure and detect in current experiments. I investigate whether quantum strategies can provide an improvement over classical protocols in the estimation of the amplification parameter. If the field is inertially prepared in the vacuum one could measure its temperature as detected by a noninertial observer and extract information about the parameter. But I would like to know if the vacuum state is the optimal probe state in an inertial frame for such a task or a better sensitivity could be achieved if the field were in a state of nonzero energy (mean photon number) from an inertial perspective. The aim is to determine the optimal input states, so that, by optimally measuring the output, one can construct an estimator for amplification channel parameter which is unbiased and has the minimum possible variance.
Squeezing-enhanced optical phase estimation can significantly improve the measurement sensitivity and effectively enhance the signal-to-noise ratio. Investigating the influence of inevitable losses and noise in quantum channels on phase measurement is of paramount importance. Here, we analyze and experimentally demonstrate the evolution of squeezing enhancement in phase measurement, particularly under a non-Markovian decoherence model characterized by a correlated Gaussian noise in a bosonic environment. We show that in a noise-added channel, where the benefits of squeezing-enhanced phase measurement are seemingly lost, the performance can be restored through the strategic introduction of classical correlated noise. This is the first, to the best of our knowledge, experimental evidence, showing that environmental memory effects can substantially enhance phase measurement performance in a squeezing-enhanced optical interferometer under the correlated Gaussian noise, providing valuable insights for practical quantum sensing in noisy environments.