Hyperentangled Bell-state analysis

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  • 14 March 2007
Abstract
It is known that it is impossible to unambiguously distinguish the four Bell states encoded in pairs of photon polarizations using linear optics. However, hyperentanglement, the simultaneous entanglement in more than one degree of freedom, has been shown to assist the complete Bell measurement of the four Bell states (given a fixed state of the other degrees of freedom). Yet introducing other degrees of freedom also enlarges the number of Bell-like states. We investigate the limits for unambiguously distinguishing a subset of all Bell-like states. In particular, we consider an additional degree of freedom to be qubit-like, such as two spatial directions, two time-bins or two orbital angular momenta, yielding 16 Bell-like states. We show that full unambiguous discrimination of these hyperentangled state is impossible. We find the optimal discrimination schemes are to group the 16 states into 7 distinguishable classes. Furthermore, we provide a procedure to uniquely distinguish any of the 16 Bell states, given two copies of it. The applications to superdense coding, quantum teleportation and fingerprinting are also discussed.

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