Heisenberg's uncertainty principle turns up everywhere in quantum mechanics. The idea is that certain types of measurements like position and momentum are paired. By measuring one of the pair, we generate uncertainty in the other. This is also referred to as quantum back-action: the thing you are measuring pushes back on the measuring system, which generates uncertainty in some other property. This fundamental idea has some serious consequences when it comes to measuring very small stuff, like gravitational waves.

There is, however, an end run around Heisenberg's uncertainty principle. If you choose to measure things that aren't paired, the precision with which we measure these properties is limited only by how good our measuring stick is. It is important to realize that these measurements are not back-action free, but that the back-action is self-canceling. In the past, researchers have decided that these types of measurements, called quantum non-demolition (QND) measurements, are either trivial or useless. Now, a paper in Physical Review X uses a more general description of QND, along with examples, to show that it is useful and that it is being applied already.

Authors Mankei Tsang and Carlton Caves start by defining the idea of a quantum-mechanics-free sub-system. The idea is that, although you have a quantum system, you can describe a certain part of it by classical dynamics. Normally this would mean that there was sufficient noise and that the quantum behavior was washed out. But this is not what they mean. What they are referring to is that the way in which a quantum system changes is often continuous and precisely described by some mathematical representation, it is only the measurement of some property that has some uncertainty. So, if you can create a measurement that has no intrinsic uncertainty, then the mathematical description looks like a classical description where everything changes and is predicted by a set of equations.

That description appears to violate the very principles of quantum mechanics, but it cannot be dismissed out of hand, because Tsang and Caves are very precise in their wording. An entire quantum system cannot be described this way, only a part of it. The back-action that would create uncertainty does not vanish but instead turns up in some property that is not of interest. Everything that can be measured without uncertainty goes in the box labeled "quantum-mechanics-free," and everything else doesn't. This cannot be done arbitrarily, though. For instance, one cannot take a position and momentum pair, and measure them without uncertainty. Instead, one has to measure some combination of positions and momentums that jointly have no uncertainty.

It is perhaps easiest to describe this in terms of one of their concrete examples: a harmonic oscillator. A harmonic oscillator can be described by the position and momentum of the particle undergoing oscillations. Any measurement on the particle position destroys knowledge of the particle momentum and vise-versa. This is a quantum mechanical system.

The same system can also be described by two harmonic oscillators, one of which has a negative mass. Now, instead of measuring the position of one particle, we have four different possible measurements that form two pairs. One pair is given by the summed position of the two particles, and their average momentum. The second pair is the separation between the particles and the difference in their momentum. When we examine these, we find that we can measure the difference in momentum and position of the two oscillators as accurately as we like, because the back action affects the sum of the particle positions and their average momentum. This is the definition of a QND, and some think it is useless because you only get the difference in position for two oscillators, not the absolute position of either of the oscillators.

You might be thinking that a harmonic oscillator with a negative mass is entirely unrealistic, but nothing could be further from the truth. A concrete example is the mechanical vibration of a mirror that forms part of an optical cavity. The light in the optical cavity consists of a series of discrete colors: the light should travel an integer number of half wavelengths as it travels from one mirror around the cavity and returns to the starting mirror. These different colors or frequencies are referred to as the modes of the cavity. If the cavity mode spacing is chosen such that it is the same as the natural frequency of the mirror's mechanical vibrations, then something very cool can happen. The movement of the mirror doppler shifts the frequency of the light, and light starts to build up in the cavity at two colors, one at a slightly redder wavelength than the original and the other at a bluer wavelength.

Let's ignore the mirror and look instead at the light. In fact, let's jump right into the picture and ride along with the light at the center frequency. In this picture, that light vanishes because we can't see it oscillating anymore. Instead we see two oscillators, the red and blue shifted light fields associated with doppler-shifts from the mirror. In this picture, riding along with the center mode, the red shifted field has a negative frequency, and to increase its amplitude involves adding a unit of negative energy. In other words, it behaves exactly like an oscillator with a negative mass. The blue shifted light field still requires positive energy to increase its amplitude, so it is a positive mass oscillator.

As a result, measurements of the amplitude and phase of either one of these light fields—which would tell you the position and momentum of the mirror—are limited by the uncertainty principle. However, the amplitude difference and phase difference can be measured with no uncertainty whatsoever. From this, the force on the mirror can be derived without uncertainty (but not the absolute position or momentum). If we go back to gravitational wave sensing, this is exactly what you want to achieve.

As mentioned earlier, the feature example is gravitational wave sensing, where very tiny fluctuations in the very fabric of space are supposed to be sensed by the shifting of a mirror. Currently, these shifts are within the noise of the measurement system, and the systems are limited by the uncertainty principle. The idea of using squeezed light to improve these instruments is not new, and that idea fits right into this description of QND.

Those of you who know something about this will be thinking "there is nothing new here." In some respects, you are absolutely right; this paper doesn't present new results as such, and in fact the examples they use are all published. So what's special? Tsang and Caves have created a more general framework. They show how disparate examples, from electron spins in a magnetic field, to vibrating mirrors, to qubit implementations can all be described by the same mathematical ideas. Knowing this, it becomes possible to construct new experimental implementations that take advantage of these QND measurements.

Physical Review X, 2012, DOI: 10.1103/PhysRevX.2.031016