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Physical Review A

Gaussianity and localization of N -qubit states

Mario Gaeta, C. Muñoz, A. B. Klimov

Published Jun 7, 2016• 8 citations
Publisher

Abstract

We analyze collective properties of $N$-qubit states. In particular, we exhaustively discuss the localization aspect of distributions in the measurement space and introduce the concept of Gaussian states in the macroscopic limit. The effect of local shifts on the localization and Gaussianity is analyzed.

DOI
10.1103/physreva.93.062107

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We analyze collective properties of NNN-qubit states. In particular, we exhaustively discuss the localization aspect of distributions in the measurement space and introduce the concept of Gaussian states in the macroscopic limit. The effect of local shifts on the localization and Gaussianity is analyzed.
We introduce a discrete QQQ function of an NNN-qubit system projected into the space of symmetric measurements as a tool for analyzing general properties of quantum systems in the macroscopic limit. For known states the projected QQQ function helps to visualize the results of collective measurements, and for unknown states it can be approximately reconstructed by measuring the lowest moments of the collective variables.
Abstract We develop a general scheme for an analysis of macroscopic N -qudit systems which includes: (a) a scheme to organize the information obtained from collective measurements in the form of distribution functions in a discrete low-dimensional space; (b) a set of collective operators appropriate for the characterization of N -qudit states; (c) two collective tomographic protocols both for general and fully symmetric N -qudit states. The example of N -qutrits is analyzed in detail and compared to the N -qubit case.
Large-scale quantum effects have always played an important role in the foundations of quantum theory.With recent experimental progress and the aspiration for quantum enhanced applications, the interest in macroscopic quantum effects has been reinforced.In this review, measures aiming to quantify various aspects of macroscopic quantumness are critically analyzed and discussed.Recent results on the difficulties and prospects to create, maintain, and detect macroscopic quantum states are surveyed.The role of macroscopic quantum states in foundational questions as well as practical applications is outlined.Finally, past and ongoing experimental advances aiming to generate and observe macroscopic quantum states are presented.
We analyze the Heisenberg limit on phase estimation for Gaussian states. In the analysis, no reference to a phase operator is made. We prove that the squeezed vacuum state is the most sensitive for a given average photon number. We provide two adaptive local measurement schemes that attain the Heisenberg limit asymptotically. One of them is described by a positive operator-valued measure and its efficiency is exhaustively explored. We also study Gaussian measurement schemes based on phase quadrature measurements. We show that homodyne tomography of the appropriate quadrature attains the Heisenberg limit for large samples. This proves that this limit can be attained with local projective von Neuman measurements.