Increasing the security of the ping-pong protocol by using many mutually unbiased bases

In this paper we propose an extended version of the ping-pong protocol and study its security. The proposed protocol incorporates the usage of mutually unbiased bases in the control mode. We show that, by increasing the number of bases, it is possible to improve the security of this protocol. We also provide the upper bounds on eavesdropping average non-detection probability and propose a control mode modification that increases the attack detection probability.

💡 Research Summary

The paper presents an enhanced version of the well‑known ping‑pong quantum direct communication protocol, focusing on improving its resistance to eavesdropping by exploiting multiple mutually unbiased bases (MUBs) in the control mode. In the original ping‑pong scheme, the control mode uses only two orthogonal bases (typically the computational Z and the Hadamard X bases) to test for tampering: the sender randomly chooses one of the two bases, the receiver measures in the same basis, and the outcomes are compared over a public channel. While this approach detects many simple attacks, it leaves a relatively high average probability that an eavesdropper (Eve) can remain undetected, especially against sophisticated intercept‑resend or collective attacks that are tailored to the limited basis set.

The authors propose to replace the two‑basis control with a set of M mutually unbiased bases, where M can be as large as d + 1 for a d‑dimensional quantum system (for qubits, d = 2, so up to three MUBs are theoretically available, and four in certain experimental constructions). Because any two vectors from different MUBs have a fixed overlap of 1/d, a measurement performed in the “wrong” basis yields completely random results, thereby maximally randomising Eve’s information gain. The protocol proceeds as follows: (1) the sender randomly selects one of the M MUBs and prepares the travel qubit accordingly; (2) the receiver measures in the same basis; (3) after the round, both parties disclose the chosen basis index and measurement outcomes over an authenticated public channel. The secret key used for encoding the actual message remains untouched, so the disclosed data alone cannot reveal the message content.

A central contribution of the paper is a rigorous derivation of an upper bound on the average non‑detection probability (P_{nd}). Assuming Eve performs an optimal attack without knowledge of the chosen basis, the probability that she guesses the correct basis is (1/M); if she guesses incorrectly, her success probability is limited to (1/d). Consequently, the bound is
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