Hybrid photonic entanglement: Realization, characterization, and applications

We show that the quantum disentanglement eraser implemented on a two-photon system from parametric downconversion is a general method to create hybrid photonic entanglement, namely the entanglement between different degrees of freedom of the photon pair. To demonstrate this, we generate and characterize a source with tunable degree of hybrid entanglement between two qubits, one encoded in the transverse momentum and position of a photon, and the other in the polarization of its partner. In addition, we show that a simple extension of our setup enables the generation of two-photon qubit-qudit hybrid entangled states. Finally, we discuss the advantages that this type of entanglement can bring for an optical quantum network.

Figure 1

(Color online) Schemes to create hybrid photonic entanglement using the (a) irreversible and (b) reversible disentanglement eraser phenomenon [16]. (c) Outline of the experimental setup that implements the scheme (a) to create and characterize HESs. For details see text. P(s): polarization (spatial) DOF; PBS: polarizing beam splitter; HWP: half-wave plate; QWP: quarter-wave plate; DC: double type-I crystals; D.S.: double slit; IF: interference filter; ${\text{D}}_j\left(j=s,i\right)$ single-photon detectors; C: coincidence counter.

Figure 2

(Color online) (a) Comparison of polarization MUBs (first row) and their counterparts in spatial DOF (third row); the second row shows their (non-normalized) logical basis representation. (b) Double slit and the QWPs that implement a SPTQ CNOT gate. (c) Truth table with the measured amplitudes. (d)–(e) Measurements (symbols) and theoretical predictions (lines) of (d) the output spatial qubits for the input given in the legend and (e) the polarization and spatial DOF entanglement for the spatial projections given in the legend. The statistical errors of (d) and (e) are on the order of the symbol size in the figures.

Figure 3

(Color online) (a)–(b) Measurements (symbols) and theoretical predictions (lines) of the Schmidt modes (a) and marginal distribution (b) of the spatial part of Eq. (4). (c)–(g) Density matrix plots obtained by maximum likelihood estimation from the experimental data. (c) Initial maximally polarization-entangled state and (d) the corresponding HES with the erasure polarization projection onto $L$. (e) Initial partially polarization-entangled state, (f) the corresponding HES with the erasure projection onto $45°$, and (g) the filtered maximally HES with the erasure projection onto $62.5°$.