Superposition and entanglement of two-mode squeezed vacuum states Amir Karimi Physics Department, Abadeh Branch, Islamic Azad University, Fars, Iran amirkarimi.phy@gmail.com; akarimi@iauabadeh.ac.ir Received 2 August 2017 Accepted 15 November 2017 Published 6 December 2017 In this paper, by using the parity operator as well as the two-mode squeezing operator, we de¯ne new operators which by the action of them on the vacuum state of the two-mode radiation ¯eld, superposition of two two-mode squeezed vacuum states and entangled two-mode squeezed vacuum states are generated. Keywords: Superposition; entangled; two-mode squeezed vacuum states. 1. Introduction Nowadays, the two concepts of superposition and entanglement have found many applications in the quantum information processing 1 including quantum computa- tion, 2 cryptography 3 and teleportation. 4 In this regard, di®erent superpositions of quantum states have been recently produced and studied. 5–7 Moreover, various entangled quantum states such as entangled coherent states 8–11 and entangled squeezed states 12–15 have been introduced and many schemes to generate such entangled states have been presented, theoretically and experimentally. 16–21 Nowadays, applications of squeezed states of radiation ¯eld such as quantum optical communication 22 and gravitational wave detection 23 have attracted a great deal of attention of researchers. Whereas much of the researches have been so far done on the single-mode squeezed states, 24–26 studies have been also conducted on the multi-mode squeezed states 27 specially two-mode squeezed vacuum states. 28,29 The two-mode squeezed vacuum states play an important role in quantum information processing because of the abilities to produce these states readily and control experimentally using available sets such as beam splitters and phase shifters and squeezers. 30 Moreover, the quantum teleportation of continuous-variable-type states ¯rst has been experimentally implemented using the two-mode squeezed International Journal of Quantum Information Vol. 16, No. 1 (2018) 1850003 (6 pages) # . c World Scienti¯c Publishing Company DOI: 10.1142/S021974991850003X 1850003-1 Int. J. Quantum Inform. Downloaded from www.worldscientific.com by UNIVERSITY OF NEW ENGLAND on 12/12/17. For personal use only.