Textbooks tell us that when one performs a quantum measurement of, say, a system in a superposition of two states, then the system will instantaneously, irreversibly, and non-unitarily transform into a system in a single state. This is clearly unsatisfactory as a description of quantum mechanics, as we believe that all other quantum dynamics occurs unitarily via the Schrödinger equation. What’s even more concerning, however, is that this notion of measurement breaks all three laws of thermodynamics [1,2]: it doesn’t conserve energy, it decreases entropy, and it makes it trivially easy to reach zero temperature.

Reconciling quantum measurement with the laws of thermodynamics will, of course, require a thermodynamic approach to modelling measurements, and this is what we set out to do with this project. We propose a new model for quantum measurements which is fully-quantum, strictly unitary, and consistent with thermodynamics, called the Measurement-Equilibration Hypothesis [3]. In short: we hypothesise that measurement is a form of equilibration in the conventional thermodynamic sense.

In standard pictures of a measurement, the system being measured is treated quantum mechanically, whilst the measuring device is considered to be classical. This is somewhat analogous to the thermodynamic notion of a small system interacting with a much larger one that has been coarse-grained — where we acknowledge we lack complete information about its microstates. In that case, one can think about the smaller system equilibrating with the larger one under some metric, most often temperature (where it is referred to as thermalisation). Equilibration is characterised by an increase in entropy up to some limiting value — it is an entropically favourable process that occurs without driving. So, rather than a model of measurement that decreases entropy, we argue that measurement is driven by an increase in entropy.

The backbone of this approach is the notion of Quantum Darwinism [4], the idea that quantum systems imprint information on their surroundings in some way, analogously to how decoherence says that surrounding environments impact systems by removing coherences from them. It has been shown [5] that for the idea to work in a way that preserves commonsense ideas about the objectivity of observations, a very specific form of Hamiltonian called a Spectrum Broadcast Structure (SBS) must be involved. We have developed a model [3] for understanding the constraints on when SBS can be acheived by uncontrolled equilibration alone, and found that it is only possible to even approximate such a structure when coarse-grainings are involved in the model of the environment. We believe that this is a first stepping-stone to a fully-realised model of measurement as equilibration, and a key to unlocking the century-old mysteries of quantum measurements.

References:

1. Yelena Guryanova, Nicolai Friis, and Marcus Huber, Ideal Projective Measurements Have Infinite Resource Costs, Quantum 4, 222 (2020), arXiv:1805.11899 [quant-ph] (2018)

2. Tiago Debarba, Gonzalo Manzano, Yelena Guryanova, Marcus Huber and Nicolai Friis, Work estimation and work fluctuations in the presence of non-ideal measurements, New J. Phys. 21 113002 (2019), arXiv:1902.08568 [quant-ph] (2019)

3. Emanuel Schwarzhans, Felix C. Binder, Marcus Huber, and Maximilian P. E. Lock, Quantum measurements and equilibration: the emergence of objective reality via entropy maximisation, arXiv:2302.11253 [quant-ph] (2023)

4. Wojciech Hubert Zurek, Quantum Darwinism Nature Physics 5.3, 181-188 (2019)

5. Thao P. Le, and Alexandra Olaya-Castro. Strong quantum darwinism and strong independence are equivalent to spectrum broadcast structure Physical Review Letters 122.1, 010403 (2019)