Two Photon Tripartite Entanglement Transfer via Time-Multiplexed Quantum Walks

TL;DR

The paper investigates how entanglement distributes in a multidimensional quantum network that combines two-photon polarization entanglement with single-photon inseparability across multiple degrees of freedom. By subjecting Bob’s photon to a time-multiplexed discrete-time quantum walk, they demonstrate entanglement transfer from A_pol–B_coin to A_pol–B_pos, effectively moving quantum correlations into a high-dimensional degree of freedom. The study introduces a generalized CHSH-type entanglement measure and a remote-conditioning protocol to quantify and verify the transfer, including nonlocal control over Bob’s position degree of freedom. The results show about 70% of the initial entanglement redistributes into the MDQN, with evidence of nonlocal entanglement between distant subsystems, underscoring the potential of MDQNs for scalable quantum information processing and networked quantum control.

Abstract

Photonic multidimensional quantum networks (MDQN), where individual subsystems are encoded using multiple degrees of freedom and photons, are an emerging platform for quantum algorithms because they offer high scalability. The distribution of non-classical and non-local correlations between the individual subsystems in an MDQN is of fundamental interest for many quantum protocols. Interestingly in an MDQN, the inseparability of two subsystems underlying entanglement can occur both between multiple distinct photons as well as between individual degrees of freedom associated with a single photon. In this work, we investigate the entanglement transfer enabled by the interplay of both entanglement between two distinct photons as well as inseparability between multiple degrees of freedom. For this purpose, we subject one photon of a polarization entangled two-photon pair to a discrete-time quantum walk introducing the position subsystem of the quantum walk as a third subsystem with qudit encoding. Here we study the resulting transfer of entanglement from the polarization degree of freedom, representing qubit encoding, towards the position degree of freedom, representing quidt encoding, via partial state tomography and correlation measurements.

Figures (6)

• Figure 1: Example of single photon inseparability generation involving a spatial and polarization degree of freedom utilizing a polarization beam splitter (PBS).
• Figure 2: Conceptual idea of the experiment combing single photon inseparability (Bob's position & Bob's coin) and two photon entanglement (Alice & Bob) by creating two polarization entangled photons separated into Alice' and Bob's subsystem respectively. A third position degree of freedom is introduced to Bob's photon via a TM-DTQW resulting in a tripartite state. The resulting entanglement between Bob's position and Alice' subsystem is investigated using projective measures and by tracing over individual subsystems.
• Figure 3: Sketch of the implemented setup consisting of a polarization entangled photon pair source in a Sagnac-Loop configuration (source), a time-multiplexed DTQW (Quantum Walk) implemented in free-space with probabilistic in- and out-coupling realized by beam splitters (BS) and polarization resolved two-photon detection (Tomography).
• Figure 4: Comparison of the experimentally measured average entanglement $E(t)$ between Alice and Bob's polarization subsystem with theoretical predictions for the first 10 DTQW steps. The measured entanglement is normalized to the initial entanglement generated between Alice' and Bob's polarization encoded photons.
• Figure 5: Simulated and measured variances $\Delta^2x$ of the average position of Bob's position distribution after $n$ DTQW steps for both classically correlated and entangled multi particle states depending on the projection angle of both Alice' and Bob's polarization DoF. The displayed variances are normalized between the minimum and maximum measured or predicted variances for each step individually.