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Zeitschrift für Naturforschung A

An Improved Ping-Pong Protocol Using Three-Qubit Nonmaximally Nonorthogonal Entangled States

Hargeet Kaur, Atul Kumar

Published May 29, 2019• 2 citations

Abstract

Abstract We analyse the ping-pong (PP) protocol [K. Bostrom and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002)] using different sets of partially entangled three-qubit states. Interestingly, our results show that the partially entangled nonorthogonal three-qubit states are more useful as resources in comparison to three-qubit maximally entangled Greenberger–Horne–Zeilinger (GHZ) states. The properties of orthogonal set of partially entangled states as resources for PP protocol, however, are similar to that of maximally entangled GHZ states – both the states are not preferable due to the vulnerability towards eavesdropping. On the other hand, partially entangled nonorthogonal basis set holds importance for transferring two-bit information, one each from a sender, to a single receiver. The protocol is further analysed for various eavesdropping attacks, and the results are compared with the use of two shared Bell pairs for two-bit information transfer. Surprisingly, the use of partially entangled nonorthogonal set of states is found to offer better qubit efficiency and increased security, as against the use of two separate maximally entangled Bell states with orthogonal basis. In addition, we also propose a mixed-state sharing protocol to further enhance the security of the PP protocol.

DOI: 10.1515/zna-2018-0448

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Abstract We analyse the ping-pong (PP) protocol [K. Bostrom and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002)] using different sets of partially entangled three-qubit states. Interestingly, our results show that the partially entangled nonorthogonal three-qubit states are more useful as resources in comparison to three-qubit maximally entangled Greenberger–Horne–Zeilinger (GHZ) states. The properties of orthogonal set of partially entangled states as resources for PP protocol, however, are similar to that of maximally entangled GHZ states – both the states are not preferable due to the vulnerability towards eavesdropping. On the other hand, partially entangled nonorthogonal basis set holds importance for transferring two-bit information, one each from a sender, to a single receiver. The protocol is further analysed for various eavesdropping attacks, and the results are compared with the use of two shared Bell pairs for two-bit information transfer. Surprisingly, the use of partially entangled nonorthogonal set of states is found to offer better qubit efficiency and increased security, as against the use of two separate maximally entangled Bell states with orthogonal basis. In addition, we also propose a mixed-state sharing protocol to further enhance the security of the PP protocol.

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A deterministic quantum communication protocol, called the ping-pong protocol, has been represented by Boström and Felbinger [Phys. Rev. Lett. 89 (2002) 187902]. Based on an entangled pair of photons, it allows asymptotically secure key distribution and quasi-secure direct communication. However, it was concluded from our previous research that the experiment realization of this protocol requires two optic paths strictly equivalent for interferometry. Here we propose an improved protocol, which is more flexible and secure for conceivable applications. Its feasibility and security are also discussed.

The "Ping-Pong" (PP) protocol is a two-way quantum key protocol based on entanglement. In this protocol, Bob prepares one maximally entangled pair of qubits, and sends one qubit to Alice. Then, Alice performs some necessary operations on this qubit and sends it back to Bob. Although this protocol was proposed in 2002, its security in the noisy and lossy channel has not been proven. In this report, we add a simple and experimentally feasible modification to the original PP protocol, and prove the security of this modified PP protocol against collective attacks when the noisy and lossy channel is taken into account. Simulation results show that our protocol is practical.

Since the first quantum secret sharing protocol based on Greenberger–Horne–Zeilinger (GHZ) states was presented by Hillery et al, dozens of quantum secret sharing protocols based on different entangled states (e.g. Bell states, d-level Bell states and GHZ states, etc) and product states have been developed. In this paper, we present a quantum secret sharing protocol, in which the genuinely maximally entangled six-qubit states, which was found recently by Borras et al, are used. An ordinary entangled state such as a Bell state or a GHZ state, etc can be used to share at most only one bit. However, according to our protocol, Alice can share three bits among three parties by a six-qubit state, which shows that our protocol is more efficient than any previous protocol.

In this paper the non-quantum method of security amplification for the ping-pong protocol with many-qubit entangled Greenberger-Horne-Zeilinger states (GHZ-states) is proposed. This method can be used in quantum cryptography and consists in invertible hashing of classical message blocks. The necessary sizes of matrices for hashing of message blocks are calculated at some values of the protocol parameters. The proposed method does not require the presence from legitimate users of any pre-established keys. Thus, the main advantage of the quantum secure direct communication protocols, namely the lack of necessity to distribute of secret key remains valid at usage of the proposed method.