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arXiv:2210.06902 · Physical Review A

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

Sanjeet Swaroop Panda, P. A. Ameen Yasir, C. M. Chandrashekar

Published Feb 13, 2023• 15 citations
arXivHTMLPDF

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.

DOI
10.1103/physreva.107.022611

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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 kkk-cycle discrete-time quantum walks (DTQW) are known to recur to its initial state after every tr{t}_{r}tr​ steps. We first present a scheme to optically realize any kkk-cycle DTQW using JJJ-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 kkk-cycle DTQW and the entanglement generated during the evolution, we present an alternate quantum direct communication protocol. The recurrence and entanglement in the kkk-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.
Quantum secure direct communication (QSDC) enables direct private message transmission over quantum channels without pre-shared keys. This paper proposes a QSDC protocol based on two-step line-based quantum walks (QWs), which involves sender Alice, receiver Bob and an untrusted third party Charlie, and three stages consisting of preparing, checking quantum channel and communicating secret messages. In the first stage, Bob generates entangled states as the desired quantum channel via one-step QW and prepares decoy photons for the subsequent security checking of the quantum channel; In the second stage, Bob first sends a sequence comprising the photons from the entangled states and Bob’s decoy photons to Alice, who forwards Bob’s decoy photons along with her own decoy photons to Charlie for measurement, with Alice and Bob verifying security by comparing the measurement outcomes; In the third stage, Alice prepares a sequence of photons as coin state for encoding messages to be communicated, which along with the prepared entangled states form a quantum teleportation system, which completes the transmission of the messages under the dominance of another-step QW. Security analyses show the suggested protocol can resist against intercept-and-resend and measure-and-resend attacks, promoting the QSDC’s practicality via QW-based entanglement generation, simplified measurement operations and security checking under the assistance of the third party Charlie.
In this article, we propose a quantum communication protocol via 2-step discrete time quantum walks with two coins on a graph of 10 vertices containing both cycles and paths. Quantum walks are known for their ability to integrate quantum mechanics dynamics like superposition and entanglement during the procedure. We calculate the total final quantum state of the system as well as the recovery operators to rescue the initial quantum state back at the receiver's location. Our work provides a fundamental block for a quantum teleportation scheme on a specific series of cycle and path graphs.
Higher channel capacity and noise elimination are the key requirements for the implementation of long-distance quantum communication. As the additional degrees of freedom (DoF) of photons can be employed to achieve higher channel capacity and security beyond the polarizations DoF of photons, the photonic qubits are always employed as the flying qubits in quantum communication and quantum information processing. Here, exploiting the multiple DoFs of photons, we present an efficient quantum secure direct communication protocol based on the coding and manipulation of qubits on both the polarization and the orbital angular momentum of photons. Also, the numerical simulation is studied to further clarify the improvement of the channel capacity and the security. It is found that the channel capacity and the error rate (caused by eavesdropping) of the QSDC protocol which encoded on the polarization DoF and the OAM DoF is significantly higher than that of coding on only polarization DoF. We believe this work could provide more evidence for the applications of higher-dimensional qubits in quantum information science.
The existing quantum secure direct communication (QSDC) protocols mainly make use of the spin angular momentum and entangled photons, to realize direct transmission of confidential information. But those protocols' capacity is low, only one-bit information. On the other hand, the orbital angular momentum (OAM) of a photon can be theoretically evaluated from minus infinity to infinity, and the angular momentum states of different orbits are orthogonal to each other. Given that, in this paper, we propose a quantum secure direct communication scheme based on OAM. Specifically, taking OAM of photons as the information carrier, the data of information is segmented and high-capacity coding in quantum secure direct communication is realized through the segmentation of sector states.
We attempt to propose the first orthogonal-state-based protocols of measurement-device-independent quantum secure direct communication and quantum dialogue employing single basis, i.e., Bell basis as decoy qubits for eavesdropping detection. Orthogonal-state-based protocols are inherently distinct from conventional conjugate-coding protocols, offering unconditional security derived from the duality and monogamy of entanglement. Notably, these orthogonal-state-based protocols demonstrate improved performance over conjugate-coding based protocols under certain noisy environments, highlighting the significance of selecting the best basis choice of decoy qubits for secure quantum communication under collective noise. Furthermore, we rigorously analyze the security of the proposed protocols against various eavesdropping strategies, including intercept-and-resend attack, entangle-and-measure attack, information leakage attack, flip attack, and disturbance or modification attack. Our findings also show that, with appropriate modifications, the proposed orthogonal-state-based measurement-device-independent quantum secure direct communication protocol can be transformed into orthogonal-state-based measurement-device-independent versions of quantum key distribution protocols, expanding their applicability. Our protocols leverage fundamentally distinct resources to close the security loopholes linked to measurement devices, while also effectively doubling the distance for secure direct message transmission compared to traditional quantum communication methods.
Abstract We attempt to propose the first orthogonal-state-based protocols of measurement-device-independent quantum secure direct communication and quantum dialogue employing single basis, i.e., Bell basis as decoy qubits for eavesdropping detection. Orthogonal-state-based protocols are inherently distinct from conventional conjugate-coding protocols, offering unconditional security derived from the duality and monogamy of entanglement. Noise imposes a major challenge to the efficient implementation of these measurement-device-independent based secure direct quantum communication protocols. Notably, these orthogonal-state-based protocols demonstrate improved performance over conjugate-coding-based protocols under certain noisy environments, highlighting the significance of selecting the best basis choice of decoy qubits for secure quantum communication under collective noise. Further, we rigorously analyze the security of the proposed protocols against various eavesdropping strategies, including intercept-and-resend attack, entangle-and-measure attack, information leakage attack, flip attack, and disturbance or modification attack. Our findings also show that, with appropriate modifications, the proposed orthogonal-state-based measurement-device-independent quantum secure direct communication protocol can be transformed into orthogonal-state-based measurement-device-independent versions of quantum key distribution and quantum key negotiation protocols, expanding their applicability. Our protocols leverage fundamentally distinct resources to close the security loopholes linked to measurement devices, while also effectively doubling the distance for secure direct message transmission compared to traditional quantum secure direct communication protocols. Additionally, we calculate the efficiency of our proposed protocols and compare them with standard versions of measurement-device-independent quantum secure direct communication protocols. Ultimately, we discuss system and operational complexity of our proposed protocols in light of experimental elements and the processes.