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Register a new userOn the complementarity of the quadrature observables
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In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon tranform of a phase space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables.
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We give a new mathematically rigorous proof for the fact that, when $S$ is a dense subset of $[0,2pi)$, the rotated quadrature operators $Q_theta$, $thetain S$, of a single mode electromagnetic field constitute an informationally complete set of observables.
As an application of the simultaneous and continuous measurement of noncommutative observables formulated in our previous paper [C. Jiang and G. Watanabe, Phys. Rev. A 102, 062216 (2020)], we propose a scheme to generate the pure ideal quadrature squeezed state in an one-dimensional harmonic oscillator system by the feedback control based on such type of measurement of noncommutative quadrature observables. We find that, by appropriately setting the strengths of the measurement and the feedback control, the pure ideal quadrature squeezed state with arbitrary squeezedness can be produced. This is in contrast to the scheme based on the single-observable measurement and the feedback control, where only nonideal squeezed state with squeezing of the measured quadrature are produced.
One of the milestones of quantum mechanics is Bohrs complementarity principle. It states that a single quantum can exhibit a particle-like emph{or} a wave-like behaviour, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system.
A which-way measurement in Youngs double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenbergs uncertainty principle: distinguishing two positions a distance s apart transfers a random momentum q sim hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohrs stance is always valid. We address this issue using the experimental technique of weak measurement. We measure a distribution for q that spreads well beyond [-hbar/s, hbar/s], but nevertheless has a variance consistent with zero. This weakvalued momentum-transfer distribution P_{wv}(q) thus reflects both sides of the debate.
The next generation of long-baseline experiments is being designed to make a substantial step in the precision of measurements of neutrino-oscillation probabilities. Two qualitatively different proposals, Hyper-K and LBNF, are being considered for approval. This document outlines the complimentarity between Hyper-K and LBNF.
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