Effective size of certain macroscopic quantum superpositions.

Area of Science:

• Quantum mechanics
• Quantum information science
• Macroscopic quantum phenomena

Background:

• Macroscopic superpositions are crucial for quantum experiments.
• States of the form |φ1⟩⊗N + |φ2⟩⊗N, with large subsystem overlap (<φ1|φ2>²=1-ε²), are common.
• Quantifying the effective size of these large N systems is challenging.

Purpose of the Study:

• To develop methods for assigning an effective particle number to macroscopic superposition states.
• To compare these methods using ideal Greenberger-Horne-Zeilinger (GHZ) states as a benchmark.
• To determine the effective size of these complex quantum states.

Main Methods:

• Proposing two distinct methods for effective particle number assignment.
• Utilizing decoherence principles in one method.
• Employing a distillation protocol in the second method.
• Using ideal GHZ states (|0⟩⊗n + |1⟩⊗n) as a reference standard.

Main Results:

• Both proposed methods successfully assign an effective particle number.
• The effective size (n) is found to be of the order of Nε².
• This result provides a quantitative measure for the complexity of macroscopic superpositions.

Conclusions:

• The study offers a novel way to characterize macroscopic quantum states.
• The effective particle number provides a useful metric, particularly for states with large N and high subsystem overlap.
• The findings are relevant for experimental proposals involving large-scale quantum systems and quantum information processing.