Experimental witness of genuine high-dimensional entanglement

Growing interest has been invested in exploring high-dimensional quantum systems, for their promising perspectives in certain quantum tasks. How to characterize a high-dimensional entanglement structure is one of the basic questions to take full advantage of it. However, it is not easy for us to catch the key feature of high-dimensional entanglement, for the correlations derived from high-dimensional entangled states can be possibly simulated with copies of lower-dimensional systems. Here, we follow the work of Kraft et al. [Phys. Rev. Lett. 120, 060502 (2018)], and present the experimental realizing of creation and detection, by the normalized witness operation, of the notion of genuine high-dimensional entanglement, which cannot be decomposed into lower-dimensional Hilbert space and thus form the entanglement structures existing in high-dimensional systems only. Our experiment leads to further exploration of high-dimensional quantum systems.

Figure 1

Experimental setup. A cw violet laser (power is 3 mW, wavelength is 404 mm) serves as the pump source and is separated by a beam displacer. Adjust the angles of HWP1-3 in the figure and the pump state can be written as $a|0\rangle +b{e}^{i{\psi }_1}|1\rangle +c{e}^{i{\psi }_2}|2\rangle +d{e}^{i{\psi }_3}|3\rangle$ after we encode $H$ ($V$) photon at upper path as $|0\rangle$ ($|1\rangle$) and $H$ ($V$) photon at lower path as $|2\rangle$ ($|3\rangle$). The pump photon is then incident to a Sagnac interferometer to pump type-II cut periodically poled potassium titanyl phosphate (ppKTP) crystal ($1\text{mm}\times 7\text{mm}\times 10\text{mm}$) and generates the state of the form as $a|00\rangle +b{e}^{i{\psi }_1}|11\rangle +c{e}^{i{\psi }_2}|22\rangle +d{e}^{i{\psi }_3}|33\rangle$. To ensure the phase stability between the two paths, the temperature of the ppKTP is controlled with a homemade temperature controller and the temperature stability is 0.001 K. The LCVRs (LCVR1 and LCVR2 are set at $0^{\circ }$ and LCVR3 is set at ${90}^{\circ }$) can be set to introduce 0 phase by properly applying voltages, thus arbitrary states of the form of $a|00\rangle +b|11\rangle +c|22\rangle +d|33\rangle$ can be prepared. This state is then distributed to Alice and Bob who finish the witness process by measuring their photon locally. BD: beam displacer; PBS: polarizing beam splitter; HWP: half wave plate; QWP: quarter wave plate; LCVR: liquid crystal variable retarder.

Figure 2

Distribution of experimental states and the value of $\text{tr}\left(\mathcal{W}\sigma \right)$. (a) The distribution of experimental states with different coefficients $a$'s and $b$'s in the case of three dimensions. The light blue region represents the states that the expectation value of $\mathcal{W}$ on them is negative. The colored dots are the experimental states which are distributed along four straight lines satisfying $a=0.65$ (pink line), $b=0.65$ (green line), $a+b=1$ (red line), and $a=b$ (blue line). (b)–(e) Experimental results of $\text{tr}\left(\mathcal{W}\sigma \right)$ along the lines in (a) respectively. Light blue lines are the theoretical value along these lines. The red dots represent the experimental results of the chosen states. (f) Experimental results of four-dimensional case. Restricting $b=c=d$, the light blue line is theoretical value of $\mathrm{tr}\left(\mathcal{W}\sigma \right)$ when scanning $a$. Experimental values are given by the red dots as well. Error bars are due to the statistics error.