Contrary to what the Heisenberg uncertainty relation might naively suggest, particle properties such as position and momentum can be simultaneously measured in some circumstances – and with high precision. We show this experimentally for the case of photon polarization properties. We also verify that while the product of the measurement precisions can be arbitrarily small, these precisions are nevertheless constrained to obey a new generalization of the Heisenberg uncertainty relation.Quantum mechanics is often thought to imply that you can precisely estimate how fast an electron is moving, or exactly where it is, but not both at the same time. The argument is that properties such as speed and position require physically incompatible devices for their precise measurement. Hence, any device used to make a simultaneous measurement will give inherently imprecise estimates.
This argument was challenged by Einstein in 1935, who gave an example where the position and speed could be accurately measured at the same time, by exploiting quantum correlations with a second particle. Note this is not in direct conflict with the well-known Heisenberg uncertainty relation, which only requires that the position and momentum cannot both be accurately predicted beforehand. However, it leaves open the important question of whether any quantum restrictions apply to simultaneous measurements.
We have experimentally verified that Einstein was correct, using polarisation properties of photons rather than position and momentum. But we also show that a high degree of joint precision does not come for free – it is only possible if the measurement outcomes are sufficiently unpredictable, as quantified by a suitable generalisation of the Heisenberg uncertainty relation.
