Table 1 Projection measurements used for quantum state tomography
From: Quantum key distribution implemented with d-level time-bin entangled photons
\(|0\rangle\) | \(\frac{1}{2}\left(\left|0\right\rangle+\left|1\right\rangle+\left|2\right\rangle+{i|}3\rangle \right)\) |
\(\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle )\) | \(\frac{1}{2}\left(\left|0\right\rangle+i\left|1\right\rangle -i\left|2\right\rangle -|3\rangle \right)\) |
\(\frac{1}{\sqrt{2}}(|2\rangle+|3\rangle )\) | \(\frac{1}{2}\left(i\left|0\right\rangle -i\left|1\right\rangle+\left|2\right\rangle -|3\rangle \right)\) |
\(|3\rangle\) | \(\frac{1}{2}\left(-\left|0\right\rangle+\left|1\right\rangle -i\left|2\right\rangle+|3\rangle \right)\) |
\(\frac{1}{\sqrt{2}}(|0\rangle -{i|}1\rangle )\) | \(\frac{1}{2}\left(-i\left|0\right\rangle+i\left|1\right\rangle -i\left|2\right\rangle -|3\rangle \right)\) |
\(\frac{1}{\sqrt{2}}(|2\rangle+{i|}3\rangle )\) | \(\frac{1}{2}\left(\left|0\right\rangle -i\left|1\right\rangle+i\left|2\right\rangle+|3\rangle \right)\) |
\(\frac{1}{2}\left(\left|0\right\rangle -\left|1\right\rangle+\left|2\right\rangle -|3\rangle \right)\) | \(\frac{1}{2}\left(\left|0\right\rangle -i\left|1\right\rangle -\left|2\right\rangle+{i|}3\rangle \right)\) |
\(\frac{1}{2}\left(\left|0\right\rangle -i\left|1\right\rangle -\left|2\right\rangle -{i|}3\rangle \right)\) | \(\frac{1}{2}\left(\left|0\right\rangle+\left|1\right\rangle -i\left|2\right\rangle -{i|}3\rangle \right)\) |
