A measurement-based measure of the size of macroscopic quantum superpositions

Abstract

Recent experiments claiming formation of quantum superposition states in near macroscopic sys- tems raise the question of how the sizes of general quantum superposition states in an interacting system are to be quantified. We propose here a measure of size for such superposition states that is based on what measurements can be performed to probe and distinguish the different branches of the state. The measure allows comparison of the effective size for superposition states in very different physical systems. It can be applied to a very general class of superposition states and reproduces known results for near-ideal cases. Comparison with a prior measure based on analy- sis of coherence between branches indicates that significantly smaller effective superposition sizes result from our measurement-based measure. Application to a system of interacting bosons in a double-well trapping potential shows that the effective superposition size is strongly dependent on the relative magnitude of the barrier height and interparticle interaction.

arXiv comment21 pages, 20 figures. Accepted by Phys. Rev. A. Replaced old version with accepted version. Significant changes and improvements, particularly to section on 1-particle measurements

References in corpus (14)

• Experimental long-lived entanglement of two macroscopic objects
• Towards quantum superpositions of a mirror
• Atom--Molecule Coherence in a Bose-Einstein Condensate
• Quantum Entanglement in Fermionic Lattices
• Quantum Superposition States of Bose-Einstein Condensates
• Quantum Correlations in Two-Fermion Systems
• Fragmentation of Bose-Einstein Condensates
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information
• Quantum Entanglement of Identical Particles
• On the effective size of certain "Schrödinger cat'' like states
• Multiple copy 2-state discrimination with individual measurements
• Path Integral Ground State with a Fourth-Order Propagator: Application to Condensed Helium
• Generation of Superposition Spin States in an Atomic Ensemble

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