Alladi Ramakrishnan Hall

Detection of true multipartite entanglement and its applications in secured communication

Ramij Rahaman

Department of Mathematics, Presidency University, Kolkata

In 1992, L. Hardy provided a no-go theorem for local hidden variables which requires only two qubits and does not require statistical inequalities, used in Bell's non-locality proof. Hardy’s proof uses a set of conditions on joint probabilities of measurement results impossible for classical (local-realistic) systems, but satisfied by predictions for a unique two-qubit entangled state. By referring to marginal probabilities, we have extended Hardy's idea and introduced a test for genuine multipartite entanglement. If all the local systems are two-levels then only a specific genuine multipartite entangled state can pass our test like in the case of original Hardy's proof. This feature finds many applications in quantum information processing tasks. Exploiting this feature, we have proposed secure quantum protocols for various communication and information processing tasks e.g., quantum key distribution, quantum random numbers generator, quantum digital signatures, quantum liar detection, quantum Byzantine agreement etc. Also, with the help of semidefinite programming, we have provided a device-independent and semi device independent security proofs of our proposed key distribution and random number generator protocols in a realistic noise scenario.

References:
R. Rahaman, M. Wiesniak & M. Zukowski, ``True Multipartite Entanglement Hardy Test", Physical Review A, vol. 90, 062338 (2014).
R. Rahaman, M. G. Parker, P. Mironowicz & M. Pawlowski, ``Device-independent quantum key distribution based on measurement inputs", Physical Review A, vol. 92, 062304 (2015).
R. Rahaman, M. Wiesniak & M. Zukowski, ``Quantum Byzantine agreement via Hardy correlations and entanglement swapping", Physical Review A, vol. 92, 042302 (2015).
R. Rahaman, ``Quantum digital signatures" (under preparation).