15.7 Conclusion
In this chapter the concepts of weak measurement and weak values were used to resolve the paradox raised by Hardy. As opposed to the orthodox analysis of the conundrum, which reached a dead end and labeled some questions as ‘unaskable’, the weak values allow us to give proper answers to these questions, along with the new possibilities of simultaneously measuring non-commuting variables, simultaneously measuring the results of counterfactual experiments, and revealing a negative number of particles.
The concepts of weak measurement and weak values arise from the two-vector formalism. The two-vector is a strict interpretation of quantum mechanics. As such, it cannot lead to experimental results that depart from the orthodox quantum analysis. Nonetheless, it has proved to be a source of ingenious ideas, paradoxes and insights.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Aharonov, P.C. Bergman, and J.L. Lebowitz: Time symmetry in the quantum process of measurement, Phys. Rev. 134, 1410–1416 (1964)
Y. Aharonov and L. Vaidman: Properties of a quantum system during the time interval between two measurements, Phys. Rev. A 41, 11–20 (1990)
Y. Aharonov and L. Vaidman: Complete description of a quantum system at a given time, J. Phys. A: Math. Gen. 24, 2315 (1991)
Y. Aharonov, D. Albert, A. Casher, and L. Vaidman: Surprising quantum effects, Phys. Lett. A 124, 199 (1987)
Y. Aharonov, S. Popescu, D. Rohrlich, and L. Vaidman: Measurements, errors, and negative kinetic energy, Phys. Rev. A 48, 4084 (1993)
A.C. Elitzur and L. Vaidman: Quantum mechanical interaction-free measurements, Found. of Phys. 23, 987–997 (1993)
L. Hardy: Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories, Phys. Rev. Lett. 68, 2981–2984 (1992)
K.J. Resch, J.S. Lundeen, and A.M. Steinberg: Experimental realization of the quantum box problem, Phys. Lett. A 324, 125 (2004)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Center for Frontier Sciences
About this chapter
Cite this chapter
Aharonov, Y., Dolev, S. (2005). New Insight into Quantum Entanglement Using Weak Values. In: Elitzur, A.C., Dolev, S., Kolenda, N. (eds) Quo Vadis Quantum Mechanics?. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26669-0_15
Download citation
DOI: https://doi.org/10.1007/3-540-26669-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22188-3
Online ISBN: 978-3-540-26669-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)