Complementarity and the uncertainty relations

Abstract

We formulate a general complementarity relation starting from any Hermitian operator with discrete non-degenerate eigenvalues. We then elucidate the relationship between quantum complementarity and the Heisenberg-Robertson's uncertainty relation. We show that they are intimately connected. Finally we exemplify the general theory with some specific suggested experiments.

9 pages, 4 figures, REVTeX, uses epsf.sty and multicol.sty

References in corpus (4)

• Optimal eavesdropping in quantum cryptography with six states
• Incoherent and Coherent Eavesdropping in the 6-state Protocol of Quantum Cryptography
• Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information
• Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process

Cited by in corpus (24)

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• Aspects of the phenomenology of interference that are genuinely nonclassical
• Generalized uncertainty relations and coherent and squeezed states
• An uncertainty view on complementarity and a complementarity view on uncertainty
• On the connection between Complementarity and Uncertainty Principles in the Mach-Zehnder interferometric setting
• Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables
• Control of quantum interference in the quantum eraser
• Experimental demonstration of continuous variable quantum erasing
• Afshar's Experiment does not show a Violation of Complementarity
• Higher order wave-particle duality
• Experimental tests of coherence and entanglement conservation
• The fundamental symmetries in the neutral kaon system -- a pedagogical choice --
• Decoherence in a double-slit quantum eraser
• Complementary reductions for two qubits
• Entropic measures of joint uncertainty: effects of lack of majorization
• State tomography for two qubits using reduced densities
• Classical and quantum complementarity
• Cloning of observables
• Uncertainty reconciles complementarity with joint measurability
• Certainty relations between local and nonlocal observables
• Imprinting interference fringes in massive optomechanical systems
• Aspects of Complementarity and Uncertainty