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Register a new userHeisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks
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We generalize past work on quantum sensor networks to show that, for $d$ input parameters, entanglement can yield a factor $mathcal O(d)$ improvement in mean squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.
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We consider a quantum sensor network of qubit sensors coupled to a field $f(vec{x};vec{theta})$ analytically parameterized by the vector of parameters $vectheta$. The qubit sensors are fixed at positions $vec{x}_1,dots,vec{x}_d$. While the functional form of $f(vec{x};vec{theta})$ is known, the parameters $vec{theta}$ are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function $q(vec{theta})$ of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.
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 determining the best choice of measurement protocol. We show that, in many cases, especially for a large number of sensors, the optimized sequential protocol results in more accurate measurements than the other strategies. In addition, in contrast to the the sensor symmetric approach, the sequential protocol is known to always be explicitly implementable. The sequential protocol is very general and has a wide range of metrological applications.
It has been suggested that both quantum superpositions and nonlinear interactions are important resources for quantum metrology. However, to date the different roles that these two resources play in the precision enhancement are not well understood. Here, we experimentally demonstrate a Heisenberg-scaling metrology to measure the parameter governing the nonlinear coupling between two different optical modes. The intense mode with n (more than 10^6 in our work) photons manifests its effect through the nonlinear interaction strength which is proportional to its average photon-number. The superposition state of the weak mode, which contains only a single photon, is responsible for both the linear Hamiltonian and the scaling of the measurement precision. By properly preparing the initial state of single photon and making projective photon-counting measurement, the extracted classical Fisher information (FI) can saturate the quantum FI embedded in the combined state after coupling, which is ~ n^2 and leads to a practical precision ~ 1.2/n. Free from the utilization of entanglement, our work paves a way to realize Heisenberg-scaling precision when only a linear Hamiltonian is involved.
The critical quantum metrology, which exploits the quantum phase transition for high precision measurement, has gained increasing attention recently. The critical quantum metrology with the continuous quantum phase transition, however, is experimentally very challenging since the continuous quantum phase transition only exists at the thermal dynamical limit. Here, we propose an adiabatic scheme on a perturbed Ising spin model with the first order quantum phase transition. By employing the Landau-Zener anticrossing, we can not only encode the unknown parameter in the ground state but also tune the energy gap to control the evolution time of the adiabatic passage. We experimentally implement the adiabatic scheme on the nuclear magnetic resonance and show that the achieved precision attains the Heisenberg scaling. The advantages of the scheme-easy implementation, robust against the decay, tunable energy gap-are critical for practical applications of quantum metrology.
We propose a W state-based protocol for anonymously transmitting quantum messages in a quantum network. Different from the existing protocols [A. Unnikrishnan, et al., Phys. Rev. Lett. 122, 240501 (2019)], the proposed protocol can be effectively implemented in the network only equipped with quantum channels and regular broadcast channels. Throughout the design procedure, we develop three sub-protocols using the W state, including the quantum collision detection protocol and the quantum notification protocol. Moreover, together with the conventional anonymous entanglement protocol, the whole anonymous communication protocol has been constructed. Finally, we examine the correctness and security of the proposed quantum anonymous communication protocol.
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