Due to the anisotropy of quantum lossy channels one must choose optimal bases of input states for best estimating them. In this paper, we obtain that the equal probability Schrödinger cat states are optimal for estimating a single lossy channel and they are also the optimal bases of input states for estimating composite lossy channels. On the other hand, by using the symmetric logarithmic derivative (SLD) Fisher information of output states exported from the lossy channels we obtain that if we take the equal probability Schrödinger cat states as the bases of input states the maximally entangled inputs are not optimal, however if the bases of the input states are not the equal probability Schrödinger cat states the maximally entangled input states may be optimal for the estimating composite lossy channel.
The use of classical multiple-pass approach for phase estimation which mimics the behavior of the N00N states, is compared with quantum techniques. It is shown that in the presence of losses its performance is significantly worse than the one of the optimal quantum strategy.
We give a simple multiround strategy that permits to beat the shot noise limit when performing interferometric measurements even in the presence of loss. In terms of the average photon number employed, our procedure can achieve twice the sensitivity of conventional interferometric ones in the noiseless case. In addition, it is more precise than the (recently proposed) optimal two-mode strategy even in the presence of loss.
We study the problem of estimating the Schwarzschild radius of a massive body using Gaussian quantum probe states. Previous calculations assumed that the probe state remained pure after propagating a large distance. In a realistic scenario, there would be inevitable losses. Here we introduce a practical approach to calculate the Quantum Fisher Informations (QFIs) for a quantum probe that has passed through a lossy channel. Whilst for many situations loss means coherent states are optimal, we identify certain situations for which squeezed states have an advantage. We also study the effect of th…
We present two complementary strategies for modeling nonlinear quantum optics in realistic integrated optical devices, where scattering loss is present. In the first strategy, we model scattering loss as an attenuation; in the second, we employ a Hamiltonian treatment that includes a mechanism for scattering loss, such as a `phantom waveguide.' These strategies can be applied to a broad range of structures and processes. As an example, we use these two approaches to model spontaneous four-wave mixing in (i) a ring-channel system and (ii) an add-drop system. Even for these well-understood syste…
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 lossy parameter, we study the energy-constrained quantum Fisher information (QFI) for generic temperature and lossy parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum…
Dose-efficient Quantum Phase Estimation in Lossy Optical Interferometry
National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University（南京大学固体微结构物理国家重点实验室和工程与应用科学学院）；School of Materials Science and Physics, China University of Mining and Technology（中国矿业大学材料科学与工程学院）
To acquire the best path-entangled photon Fock states for robust quantum optical metrology with parity detection, we calculate phase information from a lossy interferometer by using twin entangled Fock states. We show that (a) when loss is less than 50% twin entangled Fock states with large photon number difference give higher visibility while when loss is higher than 50% the ones with less photon number difference give higher visibility; (b) twin entangled Fock states with large photon number difference give sub-shot-noise limit sensitivity for phase detection in a lossy environment. This res…
We show that the minimum experimental effort to characterize the proper functioning of a quantum device scales as 2^n for n qubits and requires classical computational resources ~ n^2 2^{3n}. This represents an exponential reduction compared to the best currently available protocol, Monte Carlo characterization. The reduction comes at the price of either having to prepare entangled input states or obtaining bounds rather than the average fidelity itself. It is achieved by applying Monte Carlo sampling to so-called two-designs or two classical fidelities. For the specific case of Clifford gates…
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $φ$ whose generator is randomly sampled according to a distribution with unknown concentration $κ$, which introduces a physical source of noise. We then investigate strategies for the joint estimation of the two parameters $φ$ and $κ$ given a finite number $N$ of interactions with the phase imprinting channel. We consider both single qubit and multipartite entangled probes, and identify regions of the parameters where simul…
The derivation of ultimate limits to communication over certain quantum repeater networks have provided extremely valuable benchmarks for assessing near-term quantum communication protocols. However, these bounds are usually derived in the limit of ideal devices and leave questions about the performance of practical implementations unanswered. To address this challenge, we quantify how the presence of loss in repeater stations affect the maximum attainable rates for quantum communication over linear repeater chains and more complex quantum networks. Extending the framework of node splitting, w…
Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the lossy bosonic channel, but extension to other capacities and other Gaussian channels seems feasible. Solutions for both memoryless and memory channels are presented. It is first dealt with single use (single-mode) channel where the capacity dependence from channel's parameters is analyzed providing a full classification of the possible cases. Then it is deal…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of probes or the probing energy). Typically, it scales as 1/N^(1/2). Quantum strategies may improve the precision, for noiseless processes, by an extra factor 1/N^(1/2). For noisy processes, it is not known in general if and when this improvement can be achieved. Here we propose a general framework for obtaining attainable and useful lower bounds for the ultima…
The relaxation of a system to a steady state is a central point of interest in many attempts to advance control over the quantum world. In this paper, we consider control through instantaneous Gaussian unitary operations on the ubiquitous lossy channel, and find locally optimal conditions for the cooling and heating of a multimode Gaussian state subject to losses and possibly thermal noise. This is done by isolating the parameters that encode entropy and temperature and by deriving an equation for their evolution. This equation is in such a form that it grants clear insight into how relaxation…
Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyse different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the ent…
We consider the problem of estimating an unknown but constant carrier phase modulation $θ$ using a general -- possibly entangled -- $n$-mode optical probe through $n$ independent and identical uses of a lossy bosonic channel with additive thermal noise. We find an upper bound to the quantum Fisher information (QFI) of estimating $θ$ as a function of $n$, the mean and variance of the total number of photons $N_{\rm S}$ in the $n$-mode probe, the transmissivity $η$ and mean thermal photon number per mode ${\bar n}_{\rm B}$ of the bosonic channel. Since the inverse of QFI provides a lower bound t…
Quantum key distribution (QKD) is a pioneering quantum technology on the brink of widespread deployment. Nevertheless, the distribution of secret keys beyond a few 100 kilometers at practical rates remains a major challenge. One approach to circumvent lossy terrestrial transmission of entangled photon pairs is the deployment of optical satellite links. Optimizing these non-static quantum links to yield the highest possible key rate is essential for their successful operation. We therefore developed a high-brightness polarization-entangled photon pair source and a receiver module with a fast st…
We consider a general image sensing framework that includes many quantum sensing problems by an appropriate choice of image set, prior probabilities, and cost function. For any such problem, in the presence of loss and a signal energy constraint, we show that a pure input state of light with the signal modes in a mixture of number states minimizes the cost among all ancilla-assisted parallel strategies. Lossy binary phase discrimination with a peak photon number constraint and general lossless image sensing are considered as examples.
Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $\varepsilon$ as $\mathcal{O}(1/\varepsilon)$. In this paper, we address the task of estimating the expectation values of $M$ different observables, each to within additive error $\varepsilon$, with the same $1/\varepsilon$ dependence. We describe an approach that leverages Gilyén et al.'s quantum gradient estimation algorithm to achieve $\mathcal{O}(\sqrt{M}/\varepsilon)$ scaling…
Finding strategies to preserve quantum resources in open systems is nowadays a main requirement for reliable quantum-enhanced technologies. We address this issue by considering structured cavities embedding qubits driven by a control technique known as frequency modulation. We first study a single qubit in a lossy cavity to determine optimal modulation parameters and qubit-cavity coupling regime allowing a gain of four orders of magnitude concerning coherence lifetimes. We relate this behavior to the inhibition of the qubit effective decay rate rather than to stronger memory effects (non-Marko…
We consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds of Rubio et. al. [J. Phys. A: Math. Theor. 53 344001 (2020)] and develop a new optimized sequential protocol for measuring such functions. We compare the performance of both approaches to one another and to local protocols that do not utilize quantum entanglement, emphasizing the geometric significance of the coefficient vectors of the measured functions in …
Optimal Strategies for Multi-parameter Quantum Metrology
The Chinese University of Hong Kong（香港中文大学）；The University of Hong Kong（香港大学）；The Hong Kong Institute of Quantum Information Science and Technology（香港量子信息科学与技术研究所）
Estimating phase parameters of a three-level system interacting with two classical monochromatic fields in simultaneous and individual metrological strategies
We consider the problem of estimating multiple phases using a multi-mode interferometer. In this setting we show that while global strategies with multi-mode entanglement can lead to high precision gains, the same precision enhancements can be obtained with mode-separable states and local measurements. The crucial resource for quantum enhancement is shown to be a large number variance in the probe state, which can be obtained without any entanglement between the modes. This has important practical implications because local strategies using separable states have many advantages over global sch…
The concentration of a chiral solution is a key parameter in many scientific fields and industrial processes. This parameter can be estimated to high precision by exploiting circular birefringence or circular dichroism present in optically active media. Using the Quantum Fisher information formalism, we quantify the performance of Gaussian probes in estimating the concentration of chiral analytes. We find that bright-polarization squeezed state probes provide a quantum advantage over equally bright classical strategies that scales exponentially with the squeezing factor for a circularly birefr…
