Better measurements are inextricably linked to scientific progress. Human intelligence seemed to limit how precisely we could measure things until 1927. Later, Werner Heisenberg showed that the accuracy of some simultaneous measurements is limited by quantum physics. For example, the better you can detect a particle's position, the less certain you can be about its momentum.

In the 1980s, physicists began to see a silver line around the cloud of quantum uncertainty. They learned that quantum mechanics could be used to aid measurement rather than hinder it, the thesis of a growing discipline known as quantum metrology. In 2019, gravitational wave hunters used a quantum metrological technique called quantum compression to increase the sensitivity of LIGO detectors by 40%. Other groups have used the phenomenon of quantum entanglement to precisely measure weak magnetic fields.

It is the most controversial and confusing approach to using quantum physics to improve accuracy. Researchers use this method to capture photons or light particles containing information about a system of interest and filter some out; Photons that escape the filtering enter a detector. Experiments after the election have measured distances and angles extremely precisely over the past 15 years, implying that the rejection of photons helps in some way. "The community continues to debate its usefulness and whether it's really a quantum event [after the election]," said Noah Lupu-Gladstein, a graduate student at the University of Toronto.

Lupu-Gladstein and his co-authors have now identified the reason for the advantage in post-election measures.

According to the researchers, the new information connects different aspects of quantum physics and could be valuable in studies using sensitive photon detectors.

According to Stephan De Bievre, a mathematical physicist at the University of Lille in France who was not involved in the research, the study is "very interesting." “This connects the abstract concept of negativity to a concrete measurement approach.”

Physicists often look for a phase shift at the peaks of a wave to measure a quantity precisely. Let's say they want to find out how much the distance between two mirrors changes as a result of a passing gravitational wave distorting space-time. They started by sending a laser beam that would bounce back and forth through the mirrors. Moving a mirror shifts the peaks of laser light; Physicists evaluate this phase shift by detecting the light coming out of the system.

However, light only consists of individual photons that collectively act as a wave. Each detected photon will provide incomplete information about the phase shift (and thus mirror displacement) of the light. A precise estimate requires averaging a large number of individual photon measurements. The purpose of quantum metrology is to reduce the workload by increasing the amount of information obtained per photon.

The equations describing a particle in quantum physics do not specify where it is or how fast it is moving. Instead, they provide a probability distribution for possible particle positions and a second probability distribution for possible momentum values. However, Heisenberg's uncertainty principle prohibits precise simultaneous measurements of position and momentum (and other property pairs).

This means that unlike classical probability theory, you cannot multiply two probability distributions to create a "joint probability distribution" that represents the probability of different combinations of positions and momentum. “The system explodes when you try to describe the joint probabilities of two observables,” De Bievre added.

Quantum probabilities, on the other hand, combine in a more sophisticated way. A method independently developed by American physicist John Kirkwood in 1933 and British physicist Paul Dirac in 1945 determines the probability of various combinations of quantum properties, breaking the norm that probabilities must be positive integers. As if some combination of traits had a negative chance of occurring in the Kirkwood-Dirac quasiprobability distribution.

The Kirkwood-Dirac distribution was developed in 2020 by David Arvidsson-Shukur of the University of Cambridge, Nicole Yunger Halpern of the University of Maryland, and four other theorists. This allowed them to investigate how quantum advantage might emerge in the post-election process.

Arvidsson-Shukur and Yunger Halpern then collaborated with Toronto-based experimenters to further refine their approach. They found a quantitative relationship between the negativity of the Kirkwood-Dirac distribution and the information received per photon detected in the post-selection experiments in their new study. They showed that selection doesn't work without being negative — that is, when the observed photon properties are unrelated to the uncertainty principle and Kirkwood-Dirac distributions remain positive. However, when there is so much negativity, the amount of information increases.

You can theoretically resolve any phase change, no matter how small, with just one selected photon.

In one experiment, the researchers fired a laser through a thin slab of quartz and rotated the photons' polarization by a factor based on the slab's angle. The goal was to calculate this angle exactly. Photons were filtered using polarization sensitive optical components and these components were directed into or out of a detector depending on their polarization.

The uncertainty principle connects the different polarization directions: the more precisely you can measure how polarized a photon is along the x-axis, the less certain you can be sure of its polarization along the y-axis, for example.

The level of uncertainty in the measurement, and therefore the negative of the Kirkwood-Dirac distribution, can be changed by moving the axes of the optical components relative to each other. Once selected, photons were also affected by rotations.

They showed that the information about the angle of the plate from each detected photon grows linearly with negative order, repeating the experiment in many different configurations, as their hypothesis predicted.

Individual photons are more informative when negation is maximized, but after fewer photons are selected. The probability of a photon surviving after selection is determined by the sum of the elements of the Kirkwood-Dirac distribution; in a scatter with significant negatives, the negative and positive quasiprobability are essentially cancelled, and few photons reach the detector. Post-selection does not improve the overall amount of information carried by all photons in an experiment, due to the compromise between higher information per photon detected and fewer such photons. "We don't get a free lunch," Lupu-Gladstein said, "but we do get the food we pay for."

Even so, in some research it can be useful to use post-selection to condense all the necessary information into a few photons. Even the most advanced detectors can be overwhelmed when exposed to too many photons at once. Post-selection can help these detectors cope with the low light they can handle.

According to quantum physicist Michael Raymer of the University of Oregon, "The work offers new insights into the sensitivity of optical measurements." He warns, however, that there may be several ways to explain the origin of choice's benefit.

The Kirkwood-Dirac negation also underlies quantum behavior in situations other than metrology, such as quantum thermodynamics and fast information entanglement in black holes, as Yunger Halpern and other theorists have recently shown. According to experts, bridges in these sectors could lead to new discoveries or metrological benefits.

"One of my main goals for this work is to now open gateways for black hole researchers to say something about metrology," said Lupu-Gladstein.

Source: Quanta Magazine – Ben Brubaker

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