Scientific progress is dependent on better measurements.
Human ingenuity seemed to limit how we could measure things. Heisenberg discovered that quantum mechanics imposes a fundamental limit on the precision of some simultaneous measurements. The less certain you can be about a particle's momentum, the better you pin down its position. Heisenberg's uncertainty principle ended the dream of a perfectly knowable world.
Physicists began to see a silver lining in the cloud of quantum uncertainty. They learned that quantum mechanics can be used to aid measurement rather than hinder it. The sensitivity of the LIGO detectors was improved by 40% with the use of quantum squeezing. The phenomenon of quantum entanglement has been used to measure weak magnetic fields.
Postelection is a controversial and counterintuitive strategy for boosting precision. Researchers use particles of light that carry information about a system to filter out some of the light that isn't related to it. Over the past 15 years, the community has debated how useful postselection is and whether it is a quantum phenomenon.
Lupu-Gladstein and six co-authors have identified the source of the advantage. In a paper accepted for publication in Physical Review Letters, they point out the advantage to negative numbers that arise in calculations because of Heisenberg's uncertainty principle.
The new understanding forges links between different areas of quantum physics and could prove useful in sensitive photon detector experiments.
Stephan De Bievre, a mathematical physicist at the University of Lille in France who was not involved in the research, said that the paper is exciting.
Physicists look for a shift in the peaks of waves to measure a quantity. They want to determine the changing distance between two mirrors to signify that a passing wave has temporarily warped space-time. The laser beam will bounce back and forth between the mirrors. Physicists measure the phase shift of the laser light by detecting the light that leaves the system.
No matter how small the shift is, you can resolve it using only a single photon.
Light is composed of individual particles that behave like waves. The light's phase shift and mirror displacement will be delivered by each photon that physicists detect. A precise estimate requires a lot of individual measurements. The goal is to increase the information gained per photon.
This has been a mystery. The paper shows how to do it.
In quantum mechanics, the equations defining a particle don't say where it is or how fast it is moving. They give a probability distribution of positions at which you can observe the particle, and another probability distribution for possible values of its momentum. Heisenberg's uncertainty principle prevents simultaneous measurement of position and momentum. The way you can in classical probability theory is to divide the two probability distributions by the likelihood of different combinations of position and momentum.
The quantum probabilities combine in a more complicated way. One approach was created by the American physicist John Kirkwood and the British physicist Paul Dirac in 1933. Some combinations of properties have a negative chance of happening.
David Arvidsson-Shukur at the University of Cambridge, Nicole Yunger Halpern at the University of Maryland, and four other theorists developed a framework for describing quantum metrology experiments using the Kirkwood-Dirac distribution. They were able to explore how a quantum advantage might arise.
Arvidsson-Shukur and Halpern collaborated with experimentalists in Toronto to further develop their model. In the new paper, they found a relationship between the negative distribution of the Kirkwood-Dirac distribution and the information gained per detected photon. When measured properties of the photon aren't related by the uncertainty principle, and the distribution stays positive, postselection doesn't have an advantage. The information gain shoots up when there is a high degree of pessimism.
The researchers sent a laser through a thin quartz slab to see if it could be used to test this idea. The goal was to estimate the angle. The physicists used optical components that were sensitive to the polarization of the photon to route them into or away from a detector.
The uncertainty principle is related to different directions of polarization, like position and momentum. The experimentalists could change the amount of uncertainty in the measurement by rotating the axes of the optical components. The rotation affected which photon was selected.
The information about the angle of the slab obtained from each detected photon increased linearly with the degree of negativity, just as their theory predicted.
It is possible to make individual photons more informative by maximizing the negativity. The probability that a photon will survive a postelection depends on the amount of elements in the distribution, and the amount of quasiprobabilities that cancel out. The trade-off between increased information per detected photon and fewer photon guarantees that the total amount of information carried by all photon in an experiment is not increased.
Some experiments benefit from using postselection to concentrate all relevant information. State-of-the-art detectors overload when exposed to too many particles. The weak light that these detectors can handle can be juiced up by postselection.
Michael Raymer, a quantum physicist at the University of Oregon, said that the study provides new insights into the sensitivity of optical measurements. He cautions that there may be other ways to interpret the origin of postselection.
Recently, Yunger Halpern and other theorists showed that quantum behavior is related to other things, such as quantum thermodynamics and fast information scrambling in black holes. The researchers say that bridges could foster metrological advantages.
Lupu-Gladstein hopes that the work will open the door for people who are studying black holes to say something.
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