The uncertainty principle generally prohibits simultaneous measurements of certain pairs of observables and forms the basis of indeterminacy in quantum mechanics1. Heisenberg’s original formulation, illustrated by the famous γ-ray microscope, sets a lower bound for the product of the measurement error and the disturbance2. Later, the uncertainty relation was reformulated in terms of standard deviations3, 4, 5, where the focus was exclusively on the indeterminacy of predictions, whereas the unavoidable recoil in measuring devices has been ignored6. A correct formulation of the error–disturbance uncertainty relation, taking recoil into account, is essential for a deeper understanding of the uncertainty principle, as Heisenberg’s original relation is valid only under specific circumstances7, 8, 9, 10. A new error–disturbance relation, derived using the theory of general quantum measurements, has been claimed to be universally valid11, 12, 13, 14. Here, we report a neutron-optical experiment that records the error of a spin-component measurement as well as the disturbance caused on another spin-component. The results confirm that both error and disturbance obey the new relation but violate the old one in a wide range of an experimental parameter.
At a glance
- Wheeler, J. A. & Zurek, W. H. (eds) in Quantum Theory and Measurement (Princeton Univ. Press, 1983).
- Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172–198 (1927).
- Zur Quantenmechanik einfacher Bewegungstypen. Z. Phys. 44, 326–352 (1927).
- The uncertainty principle. Phys. Rev. 34, 163–164 (1929).
- Zum Heisenbergschen Unschärfeprinzip. Sitz. Preuss. Akad. Wiss. 14, 296–303 (1930).
- The statistical interpretation of quantum mechanics. Rev. Mod. Phys. 42, 358–381 (1970).
- On the simultaneous measurement of a pair of conjugate observables. Bell Syst. Tech. J. 44, 725–729 (1965). &
- Quantum correlations: A generalized Heisenberg uncertainty relation. Phys. Rev. Lett. 60, 2447–2449 (1988). &
- Uncertainty relations in simultaneous measurements for arbitrary observables. Rep. Math. Phys. 29, 257–273 (1991).
- in Quantum Aspects of Optical Communications. (eds Bendjaballah, C., Hirota, O. & Reynaud, S.) (Lecture Notes in Physics, Vol. 378, 3–17, Springer, 1991).
- Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurements. Phys. Rev. A 67, 042105 (2003).
- Physical content of the Heisenberg uncertainty relation: Limitation and reformulation. Phys. Lett. A 318, 21–29 (2003).
- Uncertainty relations for noise and disturbance in generalized quantum measurements. Ann. Phys. 311, 350–416 (2004).
- Universal uncertainty principle in measurement operator formalism. J. Opt. B 7, S672–S681 (2005).
- Single slit diffraction of neutrons. Phys. Rev. 179, 752–754 (1969).
- Two-photon coherent states of the radiation field. Phys. Rev. A 13, 2226–2243 (1976).
- Measurement of the quantum states of squeezed light. Nature 387, 471–475 (1997). , &
- The error principle. Int. J. Theor. Phys. 37, 2557–2572 (1998).
- The uncertainty relation for joint measurement of position and momentum. Quant. Inf. Comput. 4, 546–562 (2004).
- Heisenberg’s uncertainty principle. Phys. Rep. 452, 155–176 (2007). , &
- Observation of nonadditive mixed-state phases with polarized neutrons. Phys. Rev. Lett. 101, 150404 (2008). et al.
- Quantum Zeno effect by general measurements. Phys. Rep. 412, 191–275 (2005). &
- A double-slit ‘which-way’ experiment on the Complementarity–uncertainty debate. New J. Phys. 9, 287 (2007). et al.
- Measuring measurement–disturbance relationships with weak values. New J. Phys. 12, 093011 (2010). &
- 1988). Polarized Neutrons (Oxford Univ. Press,
- Contractive states and the standard quantum limit for monitoring free-mass positions. Phys. Rev. Lett. 51, 719–722 (1983).
- Measurement breaking the standard quantum limit for free-mass position. Phys. Rev. Lett. 60, 385–388 (1988).
- Beating the quantum limits. Nature 331, 559 (1988).
- 2000). & Quantum Computation and Quantum Information (Cambridge Univ. Press,
- 1983). States, Effects, and Operations: Fundamental Notions of Quantum Theory (Lecture Notes in Physics, Vol. 190, Springer,