Quantum Information and Communication in Multiphoton Operated Multimode Squeezed Vacuum States

Abstract

Gaussian states and Gaussian operations are extensively employed in continuous variable (CV) quantum information processing due to their mathematical tractability and ease of implemen- tation. They are used in many quantum information protocols, such as quantum teleportation, quantum dense coding, and quantum cryptography. Nonetheless, they exhibit significant limi- tations in certain quantum information and computation tasks, such as entanglement distillation and quantum error correction, because these cannot be performed with Gaussian states and Gaussian operations alone. Therefore, studying non-Gaussian states and operations became paramount to realizing universal quantum computation. newlineOne of the promising approach for generating non-Gaussian states involves photon oper- ations on multimode Gaussian states. This doctoral thesis explores few quantum information and communication related aspects of non-Gaussian states generated by performing m photon operations on the multimode states. These m photon operations can be photon addition (PA) or photon subtraction (PS) on different modes of this multimode states. The combinations of simultaneous addition and subtraction operations on such states are not considered here. The newlinem operations (PA and PS) are performed such that mi number of operations are performed on newlineeach mode i, satisfying and#931;N mi = m, where N is the total number of modes. newlineThis thesis presents two significant works. The first characterizes the behavior of quantum information theoretic measures such as Bures distance and entanglement entropy in photon op- erated two-mode squeezed vacuum (TMSV) and four-mode squeezed vacuum (FMSV) states. Here, we obtain the necessary and sufficient criteria on the bounds of these measures in termes of the number of photon operations performed on odd and even modes of TMSV and FMSV states. In case of PATMSV and PSTMSV states, m1 = m2 forms a necessary and sufficient condition on these bounds. When an equal number of photon operations are performed on odd and even modes of