Quantum direct communication protocol using recurrence in k -cycle quantum walks

Abstract

The ability of quantum walks to evolve in a superposition of distinct quantum states has been used as a resource in quantum communication protocols. Under certain settings, the k-cycle discrete-time quantum walks (DTQW) are known to recur to its initial state after every t r steps. We first present a scheme to optically realize any k-cycle DTQW using J-plate, orbital angular momentum (OAM) sorters, optical switch, and optical delay line. This entangles the polarization and OAM degrees of freedom (DoF) of a single photon. Making use of this recurrence phenomena of k-cycle DTQW and the entanglement generated during the evolution, we present an alternate quantum direct communication protocol. The recurrence and entanglement in the k-cycle walk are effectively used to retrieve and secure the information, respectively, in the proposed protocol. We investigate the security of the protocol against intercept and the resend attack. We also quantify the effect of amplitude damping and depolarizing noises on recurrence and mutual information between polarization and the OAM DoF of a single photon. Finally, we indicated an optimal attack strategy by which an Eavesdropper can tamper part of the message without revealing her presence. However, when the quantum communication channel is less noisy, any attempt by the Eavesdropper to tamper the message would end up in exposing her to the receiver.

Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers

“…Possible applications of our scheme include the circuital implementation of direct communication protocols [35,36] and quantum key distribution protocols [38] based on DTQW on the cycle. We point out that the proposed circuit does not impose constraints on the coin operator (one-qubit gate), which in principle can be changed at each time step.…”

“…Nowadays, quantum walks have proven to be a universal model for quantum computation [7][8][9][10][11], and examples of their use include algorithms for quantum search [12][13][14][15]; the solving of hard K-SAT instances [16]; graph isomorphism problems [17][18][19]; algorithms in complex networks [20,21] such as link prediction [22,23] and community detection [24,25]; and quantum simulation [26][27][28][29][30]. Furthermore, quantum communication protocols based on quantum walks have been put forward [31][32][33][34][35][36][37][38][39]. For comprehensive reviews on quantum walks and their applications, we refer the reader to [40][41][42] and to [43][44][45] for the their physical implementations.…”

On the (relation between) efficiency and secret key rate of QKD

“…Note that QSC could be used for distributing cryptographic keys as well. The QSC protocols are divided into two groups: quantum secure direct communication (QSDC) 14 – 21 and deterministic secure quantum communication (DSQC) 22 – 29 . They differ in the way of transferring messages over the communication channel.…”

“…This means that in the case of QSC the parameter R (positioned in the numerator of the efficiency expression) needs to be replaced by the overall amount of data transferred by a single QSC protocol run. Another difference between QSC and QKD is probably the number of parameters (or ) and their values 20 , 21 . This occurs due to difference between the post-processing phases of QKD and QSC.…”

The Evolution of Quantum Secure Direct Communication: On the Road to the Qinternet

“…Sheng et al [104] relaxed the requirement of two-way transmission of photons in the two-step QSDC scheme, proposing a oneway transmission to achieve QSDC. Panda et al [105] presented a QSDC protocol by utilizing quantum walks on orbital angular momentum (OAM) states.…”