Quantum dense coding by spatial state entanglement

We have presented a theoretical extended version of dense coding protocol using entangled position state of two particles shared between two parties. A representation of Bell states and the required unitary operators are shown utilizing symmetric normalized Hadamard matrices. In addition, some explicit and conceivable forms for the unitary operators are presented by using some introduced basic operators. It is shown that, the proposed version is logarithmically efficient than some other multiqubit dense coding protocols.  2003 Elsevier B.V. All rights reserved. PACS: 03.67.Hk; 89.70.+c The quantum entanglement property is providing new methods of information transfer, in some cases much more powerful than their classical counterparts. In quantum information theory, entanglement, as a key concept is used for a wide range of applications, such as dense coding [1], teleportation [2], secret sharing [3] and key distribution [4,5]. To see more about the mentioned topics and the efforts done on them, both theoretically and experimentally, one can refer to [6,7] and references therein. The quantum dense coding protocol was proposed originally by Bennett and Wiesner [1] in 1992. The protocol describes a way to transmit two bits of classical information through manipulation of only * Corresponding author. E-mail addresses: [email protected] (O. Akhavan), [email protected] (A.T. Rezakhani), [email protected]