Quantum Conditional Strategies and Automata for Prisoners’ Dilemmata under the EWL Scheme

A Symmetric Extensible Protocol for Quantum Secret Sharing

This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, a novel quantum protocol for secret sharing. At its heart, it is an entanglement-based protocol that relies on the use of maximally entangled GHZ tuples, evenly distributed among the players, endowing the spymaster with the ability to securely share a secret message with the agents. Its security stems from the fact that it is highly improbable for a malicious eavesdropper or a rogue double agent to disrupt its successful execution. It is characterized by symmetry, since all agents are treated indiscriminately, utilizing identical quantum circuits. Furthermore, it can be seamlessly extended to an arbitrary number of agents. Finally, after the completion of the quantum part of the protocol, the spymaster will have to publicly transmit some information, in order to allow the agents to unlock the secret message. This part of the protocol can be considered as an additional advantage, due to the fact that it gives the spymaster the privilege of deciding if, or when, it is the right time for the agents to unlock the secret message, after the completion of the quantum part of the protocol.

The Distributed Kolkata Paise Restaurant Game

The Kolkata Paise Restaurant Problem is a challenging game in which n agents decide where to have lunch during their break. The game is not trivial because there are exactly n restaurants, and each restaurant can accommodate only one agent. We study this problem from a new angle and propose a novel strategy that results in greater utilization. Adopting a spatially distributed approach where the restaurants are uniformly distributed in the entire city area makes it possible for every agent to visit multiple restaurants. For each agent, the situation resembles that of the iconic traveling salesman, who must compute an optimal route through n cities. We rigorously prove probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The derived equations generalize formulas that were previously known in the literature, which can be seen as special cases of our results.

A Two-Party Quantum Parliament

This paper introduces the first functional model of a quantum parliament that is dominated by two parties or coalitions, and may or may not contain independent legislators. We identify a single crucial parameter, aptly named free will radius, which can be used as a practical measure of the quantumness of the parties and the parliament as a whole. The free will radius used by the two parties determines the degree of independence that is afforded to the representatives of the parties. Setting the free will radius to zero degrades the quantum parliament to a classical one. On the other hand, setting the free will radius to its maximum value 1 makes the representatives totally independent. Moreover, we present a quantum circuit in Qiskit with which we simulate the operation of the quantum parliament under various scenarios. The experimental results allow us to arrive at some novel and fundamental conclusions that, we believe, provide new insights into the operation and the traits of a possible future quantum parliament. Finally, we propose the game “Passing the Bill,” which captures the operation of the quantum parliament and basic options available to the leadership of the two parties.

QKD Based on Symmetric Entangled Bernstein-Vazirani

This paper introduces a novel entanglement-based QKD protocol, that makes use of a modified symmetric version of the Bernstein-Vazirani algorithm, in order to achieve secure and efficient key distribution. Two variants of the protocol, one fully symmetric and one semi-symmetric, are presented. In both cases, the spatially separated Alice and Bob share multiple EPR pairs, each one qubit of the pair. The fully symmetric version allows both parties to input their tentative secret key from their respective location and acquire in the end a totally new and original key, an idea which was inspired by the Diffie-Hellman key exchange protocol. In the semi-symmetric version, Alice sends her chosen secret key to Bob (or vice versa). The performance of both protocols against an eavesdroppers attack is analyzed. Finally, in order to illustrate the operation of the protocols in practice, two small scale but detailed examples are given.

The Connection between the PQ Penny Flip Game and the Dihedral Groups

This paper is inspired by the PQ penny flip game. It employs group-theoretic concepts to study the original game and its possible extensions. In this paper, it is shown that the PQ penny flip game can be associated, in a precise way, with the dihedral group D8 and that within D8 there exist precisely two classes of equivalent winning strategies for Q. This is achieved by proving that there are exactly two different sequences of states that can guarantee Q’s win with probability 1.0. It is demonstrated that the game can be played in every dihedral group D8n, where n≥1, without any significant change. A formal examination of what happens when Q can draw their moves from the entire U(2), leads to the conclusion that, again, there are exactly two classes of winning strategies for Q, each class containing an infinite number of equivalent strategies, but all of them sending the coin through the same sequence of states as before. Finally, when general extensions of the game, with the quantum player having U(2) at their disposal, are considered, a necessary and sufficient condition for Q to surely win against Picard is established: Q must make both the first and the last move in the game.