Hyperentanglement witness

By hyperentanglement more degrees of freedom (DOF’s) of the photons are involved and entangled states spanning a high-dimension Hilbert space can be created [7, 8, 9, 10]. A hyperentangled (HE) state encoded in n DOF’s is expressed by the product of n Bell states, one for each DOF. Double Bell HE states of two photons (i.e. with n = 2) are currently realized in the laboratories and enable to perform tasks that are usually not achievable with normally entangled states. Among many applications, the realization of a complete Bell state analysis [11, 12, 13], and the recently realized enhanced dense coding[14], are particularly worth of noting. By operating with HE states of two photons and n independent DOF’s we are able to encode the information in 2n qubits. This significatively reduces the typical decoherence problems of multiphoton states based on the same number of qubits and dramatically increases the detection efficiency. HE states of increasing size are also important for the realization of advanced quantum nonlocality tests and represent a viable resource to increase the power of computation of a scalable quantum computer operating in the one-way model [15, 16]. Indeed it has been recently demonstrated that efficient 4-qubit 2-photon cluster states are easily created starting from 2-photon HE