Weak measurements show quantum uncertainty is inherent

Result clarifies role of measurement in the Heisenberg Uncertainty Principle.

Matthew Francis – Sep 12, 2012 2:33 PM | 43

Pretty sure that's the wrong Heisenberg trying to measure something. Credit: Aurich Lawson / AMC

One of the most important—and famous—results in quantum mechanics is the Heisenberg Uncertainty Principle (HUP). What is less known (at least to non-physicists) is that the HUP exists in two versions. Werner Heisenberg's original formulation stated that the act of measurement disturbs a physical system, placing strong constraints on (for example) the simultaneous measurement of both the position and momentum of a particle. A more mathematically rigorous version places inherent limits on the measurement of physical quantities—independent of whether any measurement is actually performed.

While it is often assumed that these different formulations are the same, recent theoretical results have shown the original Heisenberg measurement-based version is incomplete.

A possible violation of the original HUP has been realized experimentally by a group at the University of Toronto. Lee A. Rozema and colleagues performed a series of polarization measurements on entangled photons to determine the degree of disturbance in the system. The two possible polarization states of a photon are complementary in a quantum mechanical sense, meaning they cannot be simultaneously measured to arbitrary precision. If the original HUP is the correct one, then the physical act of measuring the polarization in one orientation will perturb the photon, affecting subsequent measurements. The researchers found that, while the later version of the HUP held, the Heisenberg HUP was violated. This result is an explicit verification that the HUP is due to intrinsic uncertainty in quantum systems rather than the effect of introducing macroscopic measurement apparatus.

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Complementary physical quantities play an important role in quantum physics. The most famous pair is position and momentum: pinpointing a particle's position means its state of motion is indeterminate. Heisenberg proposed that the act of measurement itself was responsible for the indeterminacy: using a photon of sufficient energy to locate the particle would give it a kick, making its momentum unpredictable. However, later more rigorous derivations showed that the HUP—while still concerned with the measurement of physical quantities—didn't require a specific measurement to be performed. Instead, the HUP was a statement of the intrinsic limitation of any measurement that could be taken, without needing to do an experiment. For future reference, I'll refer to the more advanced version of the HUP as the modern Heisenberg Uncertainty Principle, or MHUP.

While this distinction may seem academic, it's not. An earlier paper by Masanao Ozawa showed that Heisenberg's formulation was too stringent, which left room for sufficiently weak measurements to violate it. In other words, Ozawa's calculation showed that real measurements could violate Heisenberg's original formulation of the HUP, yet still be consistent with the MHUP. (Confession: I've conflated the two versions of the HUP when I taught the subject in the past. I'm not alone: the three quantum physics textbooks I have on my shelf do the same thing.)

The Canadian researchers used another set of complementary physical quantities instead of position and momentum: the polarization states of a photon. Precision measurement of polarization along one axis (for example) means that the measurement along another perpendicular axis is indeterminate. Not only is light polarization easier to manipulate than position or momentum, the researchers were able to use the technology of quantum entanglement—which nearly always uses photon polarization—to construct their experiment.

The authors constructed a quantum circuit, producing two photons with opposite (but unknown) polarization states. The two photons traveled down separate paths, but because their states were entangled, a measurement taken along one path revealed the state of the photon on the other path. The quantum state was measured using polarizing beam splitters (PBSs), which select photons to travel in different directions based on their polarization state. By selecting particular polarization configurations on the second photon of the entangled pair, the researchers were able to determine if the PBS had changed the state of the system—a direct test of Heisenberg's original HUP formulation.

They found that the data supported the Ozawa version of the HUP formula, with its less stringent effects from measurement perturbation. While the results were not completely in agreement with the theoretical calculation, the authors believed this is due to the imperfect nature of the initial preparation of the entangled photons. However, the results did not come close to agreement with the original Heisenberg HUP formulation.

The use of weak measurements allowed the researchers to quantify the amount of disturbance the experimental apparatus introduced. In that way, they could rule out Heisenberg's idea that it was the measurement itself that led to uncertainty. These results help clarify the role of measurement in quantum mechanics.

Physical Review Letters, 2012. DOI: 10.1103/PhysRevLett.109.100404 (About DOIs).