Kak’s three-stage protocol of secure quantum communication revisited: hitherto unknown strengths and weaknesses of the protocol

Abstract

Kak's three-stage protocol for quantum key distribution is revisited with special focus on its hitherto unknown strengths and weaknesses. It is shown that this protocol can be used for secure direct quantum communication. Further, the implementability of this protocol in the realistic situation is analyzed by considering various Markovian noise models. It is found that the Kak's protocol and its variants in their original form can be implemented only in a restricted class of noisy channels, where the protocols can be transformed to corresponding protocols based on logical qubits in decoherence free subspace. Specifically, it is observed that Kak's protocol can be implemented in the presence of collective rotation and collective dephasing noise, but cannot be implemented in its original form in the presence of other types of noise, like amplitude damping and phase damping noise. Further, the performance of the protocol in the noisy environment is quantified by computing average fidelity under various noise models, and subsequently a set of preferred states for secure communication in noisy environment have also been identified. IntroductionIn 1984, Bennett and Brassard proposed the first protocol for quantum key distribution (QKD) [1]. It succeeded to draw the attention of the cryptography community immediately as it could provide unconditional security, which is a desired but unachievable feat in the classical world. Because of these interesting features of QKD, the pioneering work of Bennett and Brassard was followed by a large number of protocols for QKD [2-5] and secure direct quantum communication [6][7][8] (where prior generation of a key is not required) (see [9] for a review). Among these schemes, only a few schemes have been realized experimentally ( [10-15] and references therein). Further, almost all the experimentally realized schemes of secure quantum communication are protocols for QKD. Only, recently a few schemes of secure direct quantum communication have been realized experimentally [14][15][16]. This fact motivated us to look for simple schemes of secure direct quantum communication that can be realized experimentally. During our investigation, we realized that there exists an experimentally implemented scheme for secure quantum communication, which can be viewed as a scheme for secure direct quantum communication, but in the original proposal as well as in the follow-up works, it has been described as a scheme for QKD. Specifically, a three-stage protocol for QKD was proposed by Kak in 2006 [17] and experimentally implemented in 2013 by Mandal et al. [18]. This scheme has certain advantages over the conventional BB84 protocol and its variants. For example, it does not require single photon source and can be implemented using multi-photon pulses [18,19]. Further, it can be modified to obtain three-stage quantum protocols for other quantum communication tasks. For example, three-stage schemes for quantum oblivious transform [20] has been proposed 1 using Kak's protocol. A quantum signature sche...

Effect of noise and topologies on multi-photon quantum protocols

“…There are several schemes for quantum secure direct communication, such as BB84 can be modified to be a quantum secure direct communication if we allow Bob to have a quantum memory. 22 However, the three-stage protocol does not require any storage capabilities and, therefore, is practical using current technology. In the next section, we'll review the effect of some of the common-noise models over the three-stage protocol.…”

“…17-21 Kak's three-stage protocol is the major focus of this study, and it is established to be one of the QKD protocols that is favorable to QSDC. 22 The two main issues restraining the development of ideal QKD setups are (1) the presence of noise in the system and (2) non-ideal photon emitters, i.e., ideal single-photon emitters are not plausible under today's technologies. The main noises affecting a practical quantum channel are amplitude damping, dephasing error, collective rotation, and bit-flip error.…”

“…The theoretical effects of a few noise models on the overall efficiency of Kak's three-stage protocol have been studied earlier. 22 We take the study further and evaluate the performance of the three-stage protocol under several new but practical noise models. Given a noisy environment, one can argue that the tolerance of the three-stage protocol to multi-photon bursts makes it akin to a repetition error-correcting code where the same photon value is transmitted several tens of times.…”

Optical designs for realization of a set of schemes for quantum cryptography

“…2.1.2 Scheme T2: Kak's three-stage scheme inspired five-stage scheme of CQD with single photons A three-stage QKD scheme proposed in the past [59] was recently shown to be able to perform secure direct quantum communication [60]. Here, we propose a three-stage scheme inspired CQD protocol, which can be viewed as a five-stage protocol of CQD.…”

“…The above status of the experimental works have motivated us to investigate possibilities of experimental realization of quantum cryptographic schemes, such as QD [6,57], CQD [58], Kak's three-stage scheme inspired direct communication scheme [59,60], CDSQC with entanglement swapping [61], which have not been experimentally realized so far. In the process, to design optical schemes for the realization of these schemes, we have perceived that the implementation requires some modifications of the original schemes.…”