@article {3495, title = {Agnostic Phase Estimation}, year = {2024}, month = {2/29/2024}, abstract = {

The goal of quantum metrology is to improve measurements\&$\#$39; sensitivities by harnessing quantum resources. Metrologists often aim to maximize the quantum Fisher information, which bounds the measurement setup\&$\#$39;s sensitivity. In studies of fundamental limits on metrology, a paradigmatic setup features a qubit (spin-half system) subject to an unknown rotation. One obtains the maximal quantum Fisher information about the rotation if the spin begins in a state that maximizes the variance of the rotation-inducing operator. If the rotation axis is unknown, however, no optimal single-qubit sensor can be prepared. Inspired by simulations of closed timelike curves, we circumvent this limitation. We obtain the maximum quantum Fisher information about a rotation angle, regardless of the unknown rotation axis. To achieve this result, we initially entangle the probe qubit with an ancilla qubit. Then, we measure the pair in an entangled basis, obtaining more information about the rotation angle than any single-qubit sensor can achieve. We demonstrate this metrological advantage using a two-qubit superconducting quantum processor. Our measurement approach achieves a quantum advantage, outperforming every entanglement-free strategy.

}, url = {https://arxiv.org/abs/2403.00054}, author = {Xingrui Song and Flavio Salvati and Chandrashekhar Gaikwad and Nicole Yunger Halpern and David R. M. Arvidsson-Shukur and Kater Murch} } @article {3485, title = {Properties and Applications of the Kirkwood-Dirac Distribution}, year = {2024}, month = {3/27/2024}, abstract = {

The most famous quasi-probability distribution, the Wigner function, has played a pivotal role in the development of a continuous-variable quantum theory that has clear analogues of position and momentum. However, the Wigner function is ill-suited for much modern quantum-information research, which is focused on finite-dimensional systems and general observables. Instead, recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in terms of arbitrary observables. This paper reviews the KD distribution, in three parts. First, we present definitions and basic properties of the KD distribution and its generalisations. Second, we summarise the KD distribution\&$\#$39;s extensive usage in the study or development of measurement disturbance; quantum metrology; weak values; direct measurements of quantum states; quantum thermodynamics; quantum scrambling and out-of-time-ordered correlators; and the foundations of quantum mechanics, including Leggett-Garg inequalities, the consistent-histories interpretation, and contextuality. We emphasise connections between operational quantum advantages and negative or non-real KD quasi-probabilities. Third, we delve into the KD distribution\&$\#$39;s mathematical structure. We summarise the current knowledge regarding the geometry of KD-positive states (the states for which the KD distribution is a classical probability distribution), describe how to witness and quantify KD non-positivity, and outline relationships between KD non-positivity and observables\&$\#$39; incompatibility.

}, url = {https://arxiv.org/abs/2403.18899}, author = {David R. M. Arvidsson-Shukur and William F. Braasch Jr. and Stephan De Bievre and Justin Dressel and Andrew N. Jordan and Christopher Langrenez and Matteo Lostaglio and Jeff S. Lundeen and Nicole Yunger Halpern} } @article {3425, title = {Quantum simulations of time travel can power nonclassical metrology}, journal = {Phys. Rev. Lett.}, volume = {131}, year = {2023}, month = {11/3/2023}, abstract = {

We construct a metrology experiment in which the metrologist can sometimes amend her input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change her input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist\&$\#$39;s winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.

}, doi = {https://doi.org/10.48550/arXiv.2207.07666}, url = {arXiv:2207.07666}, author = {David R. M. Arvidsson-Shukur and Aidan G. McConnell and Nicole Yunger Halpern} }