In an article published in Communications Physics, researchers from the Université libre de Bruxelles and the Institute for Quantum Optics and Quantum Information in Vienna present a new framework for describing physics relative to quantum reference frames, unveiling the importance of previously unrecognised “extra particles”.

In any experiment, specifying a physical quantity of interest always relies on a reference frame. For example, identifying the time at which an event happens only makes sense relative to a clock. Similarly, the position of a particle is usually defined relative to other particles. Reference frames are typically treated as classical systems, that is, they are assumed to have definite values when measured relative to other reference frames. However, as far as we know, every system is ultimately quantum. As such, it can, in principle, exist in indefinite states called quantum superpositions. What does the physical world look like when described from the perspective of a reference frame that can be in a quantum superposition? Can we define consistent rules for changing between different such perspectives?

During the past few years, there has been a surge of efforts by researchers in quantum foundations to answer these questions, which are expected to shed new light on certain aspects of physics at the intersection of quantum theory and general relativity, such as the phenomenon of indefinite causal order. One of the main difficulties that such attempts have encountered is the apparent dependence of the results of quantum reference frame transformations on the existence of remote systems, which goes contrary to the cherished locality of physical laws.

Now, Esteban Castro-Ruiz from the Institute for Quantum Optics and Quantum Information in Vienna (formerly at the Université libre de Bruxelles) and Ognyan Oreshkov from the Université libre de Bruxelles have provided a solution to this puzzle, based on a physically rigorous, operational definition of what it means to describe the world from the point of view of a quantum reference frame. Using only standard tools of quantum theory, the authors have derived a mathematically consistent way to transform between the perspectives of different quantum reference frames, which depend only on the frames and the system they wish to describe.

Their key insight is that the perspective of a reference frame should contain all the subsystems of the frame and the system that are accessible “from the inside”, that is, without access to an external reference frame. It turns out that these subsystems include more than just the system as described relative to the frame, as previously assumed. They include also a subsystem that carries information about relational properties of the frame itself. This subsystem—termed the “extra particle”—plays no role when the frame is classical, but it becomes important when the frame is in a quantum state, particularly in ensuring that transformations between different perspectives are reversible.

“In the case where the reference frame is in a classical state, the extra particle carries no information and can be ignored, which can explain why it is overlooked in our usual, textbook quantum framework”, says Esteban Castro-Ruiz. “What is surprising is that whether our reference frame is in a classical state or in a quantum superposition can be determined internally by measuring the extra particle, so it is a property that is external-frame independent, contrary to what was previously believed”.

“What I find remarkable is the simplicity of our solution. Our framework makes no hypotheses – it is derived starting from the perspective of a background reference frame using only standard quantum mechanical tools, but the results are independent of the external frame and applicable also in cases where such a frame does not exist,” emphasises Oreshkov.

The new framework lays the groundwork for a deeper, relational understanding of the role of reference frames in quantum theory, with potential applications to gauge theory and gravity.