Eur. Phys. J. D 61, 757-763 (2011)
https://doi.org/10.1140/epjd/e2010-09653-x

2N qubit “mirror states” for optimal quantum communication

¹ School of EPS, Heriot-Watt University, Edinburgh EH144, AS, UK
² Birla Institute of Technology and Science, Pilani, 333031 Rajasthan, India
³ Indian Institute of Technology Bombay, Mumbai, India
⁴ Poornaprajna Institute of Scientific Research, Devanahalli, 562110 Bangalore, India
⁵ Raman Research Institute, Sadashiva Nagar, 560012 Bangalore, India
⁶ Indian Institute of Science Education and Research (IISER) Kolkata, Salt Lake, 700106 Kolkata, India
⁷ Physical Research Laboratory, Navrangpura, 380009 Ahmedabad, India

Corresponding author: ^a prasanta@prl.res.in

Received: 23 December 2009
Revised: 5 July 2010
Published online: 14 January 2011

Abstract

We introduce a new genuinely 2N qubit state, known as the “mirror state” with interesting entanglement properties. The well known Bell and the cluster states form a special case of these “mirror states”, for N = 1 and N = 2 respectively. It can be experimentally realized using SWAP and multiply controlled phase shift operations. After establishing the general conditions for a state to be useful for various communicational protocols involving quantum and classical information, it is shown that the present state can optimally implement algorithms for the quantum teleportation of an arbitrary N qubit state and achieve quantum information splitting in all possible ways. With regard to superdense coding, one can send 2N classical bits by sending only N qubits and consuming N ebits of entanglement. Explicit comparison of the mirror state with the rearranged N Bell pairs and the linear cluster states is considered for these quantum protocols. We also show that mirror states are more robust than the rearranged Bell pairs with respect to a certain class of collisional decoherence.