Spin-orbit maximally discordant mixed states

We introduce a proposal to prepare spin-obit maximally discordant mixed states by a linear optical circuit, with quantum bits (qubits) encoded in the polarization and transverse mode degrees of freedom of photons. In particular, we discuss how to prepare nonbalanced spin-orbit entangled states, applying this technique to obtain maximally discordant mixed states. We present a simulation of the optical circuit by using the Jones matrix formalism. We performed a study of entanglement, classical, and quantum correlations. The results show excellent agreement with the underlying theory and open an alternative experimental approach for addressing quantum correlations in optical setups.

Figure 1

Proposed optical circuit. SPS stands for single-photon source, SLM for spatial light modulator, HWP@$\theta$ for half-wave plates with fast axis performing an angle $\theta$ with the horizontal, PBS for polarizer beam splitters, DP@45 for Dove prism rotated by ${45}^{\circ }$, PZT for piezoelectric transducer, NF for neutral filter, M2 and M3 for holographic masks for preparation of the ${\mathrm{HG}}_{0,1}$ and ${\mathrm{HG}}_{1,0}$ modes, and M for mirrors.

Figure 2

Density probability of detection of a photon in the output transverse plane of the preparation circuit for different weights $\epsilon$. The calculation was performed for rank-2 (R2) and rank-3 (R3) states. We used $m=1/4$ for the rank-3 state.

Figure 3

Correlations for rank-2 states ($p=0.5$) as a function of the weight $\epsilon$. Dots are the results for the calculation from the state simulated by the preparation optical circuit using the Jones formalism. The lines are theoretical predictions of quantum theory. Classical correlation $C$: Circles dots and dashed line. Concurrence $C^{\prime }$: Squares dots and dotted line. Quantum discord $Q$: Triangles dots and solid line.

Figure 4

Correlations for rank-3 states ($p=m=0.5$) as function of the weight $\epsilon$. Dots are the results for the calculation from the state simulated by the preparation optical circuit using the Jones formalism. The lines are theoretical predictions of quantum theory. Classical correlation $C$: Circles dots and dashed line. Concurrence $C^{\prime }$: Squares dots and dotted line. Quantum discord $Q$: Triangles dots and solid line.

Figure 5

Quantum discord versus classical correlation for a sample of rank-2 (gray dots) and rank-3 (black circles) states.