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arXiv:1106.0062

Comment on "Quantification of Macroscopic Quantum Superpositions within Phase Space"

Jiangbin Gong

Published Jun 1, 2011• 5 citations
arXivHTMLPDF

Abstract

The phase space measure proposed by Lee and Jeong [PRL 106, 220401 (2011)] is shown to be closely related to a well-studied measure in the literature. For pure states, the newly proposed measure is equivalent to an old measure; for mixed states, some discussions are given.
DOI
10.48550/arxiv.1106.0062

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Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a harmonious manner: the degree of quantum coherence and the effective size of the physical system that involves the superposition. It enjoys remarkably good analytical and algebraic properties. It turns out to be the most general and inclusive measure ever proposed that it can be applied to any types of multipartite states and mixed states represented in phase space.
We consider the controlled quantum teleportation performed on a single copy of entangled three-qubit pure states and show how the fidelity of teleportation and the control power are related to the tripartite entanglement measures, namely, three-tangle and genuine concurrence. We characterize the states with extreme properties, and use them to derive tight lower and upper bounds on both the teleportation fidelity and control power for a given amount of entanglement. Furthermore, we discuss the usefulness of these two quantities for experimental detection and/or quantification of tripartite entanglement. In particular, we present the results which imply that the control power cannot be considered as a candidate for a degree of three-qubit entanglement complementary to the three-tangle as conjectured recently [K. Jeong, J. Kim, and S. Lee, Phys. Rev. A 93, 032328 (2016)]. Furthermore, we prove a mutual relation between teleportation fidelity and control power which provides attainable limits of the controller's authority for existing controlled teleportation schemes. Although those relations are derived for pure states, their extensions for mixed states are also examined.