[Paper Review] Entanglement Detection with Single Hong-Ou-Mandel Interferometry

Chang Jian Kwong, Simone Felicetti+2 more|arXiv (Cornell University)|Jun 1, 2016

Optical Polarization and Ellipsometry3 citations

TL;DR

This paper proposes a minimal-resource method for detecting all entangled quantum states using a single Hong-Ou-Mandel (HOM) interferometer with only two detectors, regardless of system dimension or number of modes. By leveraging quantum state joining and orbital angular momentum (OAM) encoding, the scheme estimates fidelity between two pure states to detect entanglement without full tomography, demonstrating that entanglement detection requires fewer resources than quantum state tomography.

ABSTRACT

Entanglement is not only fundamental for understanding multipartite quantum systems but also generally useful for quantum information applications. Despite much effort devoted so far, little is known about minimal resources for detecting entanglement and also comparisons to tomography which reveals the full characterization. Here, we show that all entangled states can in general be detected in an experimental scheme that estimates the fidelity of two pure quantum states. An experimental proposal is presented with a single Hong-Ou-Mandel interferometry in which only two detectors are applied regardless of the dimensions or the number of modes of quantum systems. This shows measurement settings for entanglement detection are in general inequivalent to tomography: the number of detectors in quantum tomography increases with the dimensions and the modes whereas it is not the case in estimation of fidelity which detects entangled states.

Motivation & Objective

• To develop an experimental scheme for detecting all entangled quantum states with minimal measurement resources.
• To demonstrate that entanglement detection does not require full quantum state tomography, which scales poorly with system size.
• To show that fidelity estimation via HOM interferometry can serve as a universal entanglement detection tool across arbitrary-dimensional and multimode systems.
• To enable feasible experimental implementation using current photonic technologies, including quantum state joining and OAM encoding.

Proposed method

• The method uses a single HOM interferometer with only two detectors to estimate the fidelity between two pure quantum states.
• It employs quantum state joining to merge two photonic qubits into a single photon, encoding information in polarization and path degrees of freedom.
• Orbital angular momentum (OAM) encoding is implemented using spatial light modulators (SLMs) to map path information onto OAM states.
• A post-selection step is applied to select specific output states (e.g., horizontal polarization in paths a and c), yielding a four-dimensional output state in polarization and path.
• The scheme relies on the bunching effect in bosonic systems, where indistinguishable photons interfere at a beam splitter, enabling fidelity estimation.
• Entanglement is detected by observing negative expectation values of entanglement witnesses derived from the fidelity estimation, without requiring full tomographic reconstruction.

Experimental results

Research questions

• RQ1 Can entanglement be detected without performing full quantum state tomography?
• RQ2 Is it possible to detect all types of entangled states using a fixed number of detectors, independent of system dimension or mode count?
• RQ3 Can fidelity estimation via a single HOM interferometer serve as a universal entanglement detection protocol?
• RQ4 What experimental techniques enable minimal-resource entanglement detection using current photonic technologies?

Key findings

• The proposed scheme detects all entangled states using only two detectors, regardless of the Hilbert space dimension or number of modes.
• The method achieves universal entanglement detection by estimating the fidelity between two pure quantum states via a single HOM interferometer.
• Post-selection success probability for the required state preparation is 1/32, which is feasible with current photonic technologies.
• The scheme avoids the resource scaling of quantum tomography, where detector count increases with system size.
• Entanglement witnesses derived from fidelity estimation can detect entanglement without requiring a complete set of measurements for tomography.
• The use of quantum state joining and SLM-based OAM encoding enables efficient encoding of multi-dimensional information in a single photon.