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Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into ensemble of pure states of Schmidt rank 1 or 2. That is, the Schmidt number of the density matrix must be equal to or greater than 3.
Recently, atomic ensemble and single photons were successfully entangled by using collective enhancement [D. N. Matsukevich, textit{et al.}, Phys. Rev. Lett. textbf{95}, 040405(2005).], where atomic internal states and photonic polarization states we
So far experimental confirmation of entanglement has been restricted to qubits, i.e. two-state quantum systems including recent realization of three- and four-qubit entanglements. Yet, an ever increasing body of theoretical work calls for entanglemen
Quantum complementarity states that particles, e.g. electrons, can exhibit wave-like properties such as diffraction and interference upon propagation. textit{Electron waves} defined by a helical wavefront are referred to as twisted electrons~cite{uch
We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefficient matrices of the states, we obtain explicitly two equivalent classes of
It is known that beyond $2 otimes 2$ and $2 otimes 3$ dimensional quantum systems, Peres-Hordecki criterion is no longer sufficient as an entanglement detection criterion as there are entangled states with both positive and negative partial transpose