Asymmetric quantum dialogue in noisy environment

Abstract

A notion of asymmetric quantum dialogue (AQD) is introduced. Conventional protocols of quantum dialogue are essentially symmetric as both the users (Alice and Bob) can encode the same amount of classical information. In contrast, the scheme for AQD introduced here provides different amount of communication powers to Alice and Bob. The proposed scheme, offers an architecture, where the entangled state and the encoding scheme to be shared between Alice and Bob depends on the amount of classical information they want to exchange with each other. The general structure for the AQD scheme has been obtained using a group theoretic structure of the operators introduced in (Shukla et al., Phys. Lett. A, 377 (2013) 518). The effect of different types of noises (e.g., amplitude damping and phase damping noise) on the proposed scheme is investigated, and it is shown that the proposed AQD is robust and uses optimized amount of quantum resources.The birth of quantum cryptography in 1984 [1], followed by its variants steadily paved way for various quantum communication schemes, thereby, establishing its manifold applications (see [2] and references therein). Initial protocols [1,3,4,5] of secure quantum communication were restricted to the designing of protocols for quantum key distribution (QKD), which enables a sender (Alice) to share (distribute) a key with a receiver (Bob). It was later realized that a preshared (pre-distributed) key is not essential for secure quantum communication, and several schemes for secure direct quantum communication were proposed [6,7,8,9,10,11]. These schemes of secure direct quantum communication were mainly of two types: quantum secure direct communication (QSDC) and deterministic secure quantum communication (DSQC). In a QSDC scheme, the receiver can decode an information encoded by the sender without any additional information (classical communication) [6,7,8]. In contrast, in a scheme for DSQC, the receiver requires at least one bit of classical information to decode each bit of the message encoded by the sender [9,10]. Different variants of DSQC and QSDC protocols have been studied in the recent past. Specifically, controlled DSQC has been studied in much detail in the recent past ([11] and references therein). Interestingly, the schemes of DSQC and QSDC are one way schemes in the sense that these schemes only allow Alice to communicate a message to Bob, but does not allow Bob to do the same. In contrast, in daily life, one often need bidirectional communication, where two parties can simultaneously communicate messages to each other, an example been classical communication via telephone. Keeping this in mind, a scheme for simultaneous bidirectional quantum communication was introduced by Ba An [12] in 2004, and was referred to as "quantum dialogue (QD)". However, it was found that the Ba An scheme was insecure under intercept-resend attack [9]. In Ref. [9], an effort was made to modify the original Ba An scheme to provide a secure * 1 scheme for QD. However the effort was not successful a...

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