[Paper Review] Quantum Tomography of Inductively-Created Large Multiphoton States

E. Megidish, Ayelet Halevy+3 more|arXiv (Cornell University)|Dec 11, 2017

Quantum Mechanics and Applications4 citations

TL;DR

This paper presents a resource-efficient method to fully characterize large multiphoton Greenberger-Horne-Zeilinger (GHZ) states generated via inductive fusion of entangled photon pairs. By experimentally tomographing the two-photon source and the fusion process, the authors calculate the full density matrices of GHZ states with up to twelve photons, achieving 85.4% fidelity for four photons and maintaining genuine multiphoton entanglement up to ten photons with fidelity above 50%.

ABSTRACT

The generation of quantum entangled states of many particles is a central goal of quantum information science. Characterizing such states is a complex task that demands exponentially large resources as particles are being added. Previously, we demonstrated a resource efficient source that can generate, in principal, entanglement between any number of photons. This source recursively fuse photon pairs generated by a pulsed laser into a multiphoton entangled state. In the current work, we perform quantum state tomography on the photon pair source and quantum process tomography on the fusion operation. As a result, the full quantum Greenberger-Horne-Zeilinger (GHZ) state of any number of photons can be calculated. We explore the prospects of our scheme and calculate nonlocality and genuine extit{N}-photon entanglement thresholds for states with up to twelve photons.

Motivation & Objective

• To overcome the exponential resource scaling of standard quantum state tomography for large multiphoton entangled states.
• To enable full characterization of high-photon-number GHZ states without requiring experimental detection of the full state.
• To verify genuine N-photon entanglement and nonlocality in large-scale multiphoton systems.
• To demonstrate the feasibility of generating and characterizing multiphoton entangled states beyond current experimental limits.

Proposed method

• Perform quantum state tomography (QST) on the two-photon entangled source to reconstruct its density matrix.
• Conduct quantum process tomography (QPT) on the two-photon fusion operation to reconstruct the process matrix.
• Use the experimentally characterized two-photon state and fusion process to analytically calculate the full density matrix of any potentially generated GHZ state.
• Apply maximal likelihood estimation and bootstrap Monte Carlo simulations to assess errors and fidelity of reconstructed states.
• Calculate nonlocality thresholds using Mermin and Żukowski Bell inequalities to assess violation of local realism.
• Use time delays and polarization beam splitters to enable sequential fusion of photon pairs into larger entangled states.

Experimental results

Research questions

• RQ1 Can the full density matrix of a large multiphoton GHZ state be calculated without direct experimental measurement of the full state?
• RQ2 What is the fidelity of the reconstructed GHZ state for increasing photon numbers, and does it exceed the threshold for genuine N-photon entanglement?
• RQ3 To what extent does the system violate local realism, and how does this violation scale with photon number?
• RQ4 How do experimental imperfections such as photon distinguishability and polarization errors affect the fidelity of the reconstructed states?
• RQ5 Can the fusion process be used to generate and characterize states with more than ten photons, despite low detection rates?

Key findings

• The four-photon GHZ state reconstructed from the source and fusion process achieved a fidelity of (85.4 ± 0.2)% with the ideal state.
• The six-photon GHZ state showed a fidelity of (74.3 ± 0.4)% with the ideal state, confirming GHZ-like correlations.
• Genuine multiphoton entanglement was confirmed up to ten photons, with fidelity above the 50% threshold required for genuine N-photon entanglement.
• The fidelity for the twelve-photon state was (49.3 ± 0.65)%, just below the 50% threshold, indicating near-threshold performance.
• The calculated interference visibility for all photons measured in the |p/m⟩ basis exceeded the Mermin and Żukowski nonlocality thresholds, confirming violation of local realism for all photon numbers studied.
• The method enables full characterization of GHZ states with up to twelve photons using only two-photon tomography, bypassing the exponential resource scaling of standard quantum state tomography.