[Paper Review] Entanglement and Non-locality in a Micro-Macroscopic system

F. De Martini, Fabio Sciarrino+1 more|ArXiv.org|Apr 2, 2008

Quantum Information and Cryptography46 references3 citations

TL;DR

This paper demonstrates experimentally the entanglement of a single photon (microscopic system) with a macroscopic superposition state of approximately 35,000 photons, generated via quantum-injected optical parametric amplification (QI-OPA). The system violates Bell's inequality, confirming nonlocality in a micro-macro quantum system and providing direct evidence of quantum non-separability across scales.

ABSTRACT

In recent years two fundamental aspects of quantum mechanics have attracted a great deal of interest, namely the investigation on the irreducible nonlocal properties of Nature implied by quantum entanglement and the physical realization of the 'Schroedinger Cat'. In the present work a macro - state consisting of about 3.5 x 10^4 photons in a quantum superposition and entangled with a far apart single - photon state is generated. Then, the non-separability of the overall micro-macro system is demonstrated and the corresponding Bell's inequalities are found to be violated. Precisely, an entangled photon pair is created by a nonlinear optical process, then one photon of the pair is injected into an optical parametric amplifier operating for any input polarization state, i.e. into a phase-covariant cloning machine. Such transformation establishes a connection between the single photon and the multi particle fields. We then demonstrate the non-separability of the bipartite system by adopting a local filtering technique within a positive operator valued measurement.

Motivation & Objective

• To experimentally realize a quantum system entangling a single photon (microscopic) with a macroscopic superposition of ~3.5×10⁴ photons.
• To test the nonlocal correlations predicted by quantum mechanics in a system where one party is macroscopic, challenging classical intuitions about quantum-classical boundaries.
• To verify the violation of Bell's inequality in a micro-macro entangled system, thereby ruling out local hidden variable theories for such large-scale quantum states.
• To explore the quantum-to-classical transition by observing how quantum features persist in macroscopic systems through amplification and measurement.
• To demonstrate a scalable platform for quantum information processing using macroscopic quantum states generated via QI-OPA.

Proposed method

• Entangled photon pairs were generated via spontaneous parametric down-conversion (SPDC) in a nonlinear crystal, producing a singlet state |Ψ⁻⟩.
• One photon from the pair was injected into a high-gain optical parametric amplifier (OPA) acting as a phase-covariant cloning machine, transforming the single-photon state into a macroscopic superposition of Fock states.
• The amplification process, termed quantum-injected optical parametric amplification (QI-OPA), generated a macroscopic quantum state involving N ≈ 3.5×10⁴ photons in superposition.
• Non-separability of the resulting micro-macro entangled state was confirmed using a local filtering technique within a positive operator-valued measure (POVM) framework.
• Bell-type inequalities were tested using four measurement bases: {π₊, π₋} and {πᴿ, πᴸ}, with phase shifts controlled via a Soleil-Babinet compensator.
• Coincidence rates and visibility were measured over 5 hours, averaging 4000 events per data point, with phase-covariance ensured by electronic filtering independent of input phase.

Experimental results

Research questions

• RQ1 Can a single-photon quantum state be entangled with a macroscopic superposition of photons (~3.5×10⁴) while preserving nonlocal correlations?
• RQ2 Does the resulting micro-macro entangled state violate Bell's inequality, thereby ruling out local hidden variable models?
• RQ3 How does the quantum-injected optical parametric amplifier (QI-OPA) enable the creation of a macroscopic superposition from a single-photon input?
• RQ4 To what extent do quantum features such as nonlocality persist in systems of increasing size, approaching the classical domain?
• RQ5 Can this setup be upgraded to generate entanglement between two macroscopic superpositions, enabling macro-macro nonlocality?

Key findings

• The experiment successfully generated a micro-macro entangled state with a macroscopic component of approximately 3.5×10⁴ photons in superposition.
• The system exhibited a visibility of 97% in the measured coincidence patterns, indicating high-fidelity quantum state preparation and preservation.
• Bell’s inequality was violated with a value of S = 2.48 ± 0.06, exceeding the classical limit of 2, confirming nonlocal correlations in the micro-macro system.
• The electronic filtering system demonstrated phase-covariance, with a constant filtering probability P_fil across all input phases, ensuring measurement fairness.
• Theoretical photon number probability distributions (Figure 11) confirmed the symmetric, entangled nature of the macroscopic state |Φ⁺,⁻⟩ with dominant Fock states near (2i+1, 2j+1) for i,j ≈ 0–10.
• The QI-OPA process enabled the creation of a macroscopic quantum state from a single-photon input, preserving quantum coherence and enabling nonlocality testing.