Distilling Quantum Particles

This is a story about distillation—a process that has kept my family busy for generations.

My great, great, great, great grandfather was known as Brännvinskungen, loosely translated as the Vodka King. This “royal” ancestor of mine lived in the deepest forests of Småland, Sweden; the forests that during his time would populate the US state of Minnesota with emigrants fleeing the harshest lands of Europe. The demand for alcoholic beverages among their inhabitants was great. And the Vodka King had refined both his recipe and the technology to meet the demand. He didn’t claim to compete with big Stockholm-based companies in terms of quality or ambition. Nevertheless, his ability to, using simple means and low cost, turn water into (fortified) wine earned him his majestic title.

I’m not about to launch the concept of quantum vodka. Instead, I’m about to tell you about my and my stellar colleagues’ results on the distillation of quantum particles. In the spirit of the Vodka King, I don’t intend to compete with the big players of quantum computing. Instead, I will describe how a simple and low-cost method can distil information in quantum particles and improve technologies for measurements of physical things. Before I tell you about how quantum distillation can improve measurements, I need to explain why anyone would use quantum physics to do measurements in the first place, something known as quantum metrology.

According to Wikipedia, “metrology is the scientific study of measurement”. And just about any physical experiment or technology relies on measurements. Quantum metrology is the field of using quantum phenomena, such as entanglement, to improve measurements [1]. The ability to quantum-boost technologies for measurements has fostered a huge interest in quantum metrology. My hope is that speedometers, voltmeters, GPS devices and clocks will be improved by quantum metrology in the near future. 

There are some problems to overcome before quantum metrology will make it to the mainstream. Just like our eyes on a bright day, quantum-measurement devices saturate (are blinded) if they are subjected to overly intense beams of quantum particles. Very often the particle detectors are the limiting factor in quantum metrology: one can prepare incredibly strong beams of quantum particles, but one cannot detect and access all the information they contain. To remedy this, one could use lower-intensity beams, or insert filters just before the detectors. But ideally, one would distil the information from a large number of particles into a few, going from high to low intensity without losing any information. 

Figure 1: Rough workings of non-polarising sunglasses (left), polarising sunglasses (middle) and the new quantum filter (right). Light-particles are represented by bottles, and information by the bottles’ content.

Collaborators and I have developed a quantum filter that solves this precise problem [2, 3]. (See this blog post for more details on our work.) Our filter provides sunglasses for quantum-metrology technologies. However, unlike normal sunglasses, our quantum filters increase the information content of the individual particles that pass through them. Figure 1 compares sunglasses (polarising and non-polarising) with our quantum filter; miniature bottles represent light-particles, and their content represents information.

  • The left-most boxes show the effect of non-polarising sunglasses, which can be used when there is a strong beam of different types of light particles that carry different amounts of information. The sunglasses block a fraction of the light particles. This reduces glare and avoids eyes’ being blinded. However, information is lost with the blocked light particles. 
  • When driving a car, you see light particles from the surroundings, which vibrate both horizontally and vertically. The annoying glare from the road, however, is made of light particles which vibrate predominantly horizontally. In this scenario, vertical light carries more information than horizontal light. Polarising sunglasses (middle boxes) can help. Irritating horizontal light particles are blocked, but informative vertical ones aren’t. On the level of the individual particles, however, no distillation takes place; the information in a vertical light particle is the same before and after the filter.
  • The right-most boxes show the workings of our quantum filter. In quantum metrology, often all particles are the same, and all carry a small amount of information. Our filter blocks some particles, but compresses their information into the particles that survive the filter. The number of particles is reduced, but the information isn’t.

Our filter is not only different to sunglasses, but also to standard distillation processes. Distillation of alcohol has a limit: 100%. Given 10 litres of 10% wine, one could get at most 1 litre of 100% alcohol, not ½ litres of 200% alcohol. Our quantum filters are different. There is no cap on how much information can be distilled into a few particles; the information of a million particles can all be compressed into a single quantum particle. This exotic feature relies on negativity [4]. Quantum things cannot generally be described by probabilities between 0% and 100%, sometimes they require the exotic occurrence of negative probabilities. Experiments whose explanations require negative probabilities are said to possess negativity. 

Figure 2: Quantum metrology with laser-light particles. (a) Without quantum filter. (b) With quantum filter.

In a recent theory-experiment collaboration, spearheaded by Aephraim Steinberg’s quantum-optics group, our multi-institutional team designed a measurement device that can harness negativity [5]. Figure 2 shows an artistic model of our technology. We used single light particles to measure the optical rotation induced by a piece of crystal. Light particles were created by a laser, and then sent through the crystal. The light particles were rotated by the crystal: information about the degree of rotation was encoded in the particles. By measuring these particles, we could access this information and learn what the rotation was. In Figure 2(a) the beam of particles is too strong, and the detectors do not work properly. Thus, we insert our quantum filter [Figure 2(b)]. Every light particle that passed our quantum filter carried the information of over 200 blocked particles. In other words, the number of particles that reached our detector was 200 times less, but the information the detector received stayed constant. This allowed us to measure the optical rotation to a level impossible without our filter. 

Our ambition is that our proof-of-principle experiment will lead to the development of filters for other measurements, beyond optical rotations. Quantum metrology with light particles is involved in technologies ranging from quantum-computer calibration to gravitational-wave detection, so the possibilities for our metaphorical quantum vodka are many.

David Arvidsson-Shukur, Cambridge (UK), 14 April 2022

David is a quantum researcher at the Hitachi Cambridge Laboratory. His research focuses on both fundamental aspects of quantum phenomena, and on practical aspects of bringing such phenomena into technologies.

[1] ‘Advances in quantum metrology’, V. Giovannetti, S. Lloyd, L. Maccone, Nature photonics, 5, 4, (2011), https://www.nature.com/articles/nphoton.2011.35

[2] ‘Quantum Advantage in Postselected Metrology’, D. R. M. Arvidsson-Shukur, N. Yunger Halpern, H. V. Lepage, A. A. Lasek, C. H. W. Barnes, and S. Lloyd, Nature Communications, 11, 3775 (2020), https://doi.org/10.1038/s41467-020-17559-w

[3] ‘Quantum Learnability is Arbitrarily Distillable’, J. Jenne, D. R. M. Arvidsson-Shukur, arXiv, (2020), https://arxiv.org/abs/2104.09520

[4] ‘Conditions tighter than noncommutation needed for nonclassicality’, D. R. M. Arvidsson-Shukur, J. Chevalier Drori, N. Yunger Halpern, J. Phys. A: Math. Theor., 54, 284001, (2021), https://iopscience.iop.org/article/10.1088/1751-8121/ac0289

[5] ‘Negative quasiprobabilities enhance phase-estimation in quantum-optics experiment’, N. Lupu-Gladstein, Y. B. Yilmaz, D. R. M. Arvidsson-Shukur, A. Broducht, A. O. T. Pang, Æ. Steinberg, N. Yunger Halpern, P.R.L (in production), (2022), https://arxiv.org/abs/2111.01194