###### Abstract
The technological challenges and intricate implementation issues, such as the complexity of operations and the ability to control and measure the entangled states accurately, are not in the least underestimated, but from the point of view of an active quantum practitioner that is given a working apparatus, they may be assumed solved at least to a certain satisfactory degree. To make its presentation more easygoing for the reader, we describe it as a quantum game, something quite usual in the literature. The role of the millionaires is assumed by the famous [PERSON] and her clones, which star alongside [PERSON] and [PERSON], who play the two third parties that are required for the secure implementation of the protocol. Quantum games were introduced in the two pioneering works [55; 56] that go back to 1999. Since then, they have gained remarkable acceptance, mainly due to the fact that quantum strategies are often superior to classical ones [57; 58; 59; 60]. The famous Prisoner's Dilemma game provides a convincing example in this regard [56]. This article introduces a novel protocol, aptly named GHZ\({}_{3}\)MQPEC, that accomplishes a multiparty quantum private comparison relying exclusively on \(|GHZ_{3}\rangle\) triplets. In designing this protocol, our fundamental concern has been to come up with an algorithm that can be easily run on today's quantum computers. We achieved this aim by utilizing only \(|GHZ_{3}\rangle\) triplets for any number \(n\) of millionaires. While more complex multiparticle entangled states, not to mention high-dimensional quantum states, are possible, they are difficult to generate with existing quantum technology, leading to an extended preparation time and complexity, especially in cases where the number of players becomes arbitrarily large. Of course, there is a plethora of classes of entangled states, such as W states, cluster states, and graph states, to name just a few. Within the circuit model paradigm, GHZ states can be easily produced, given a powerful enough quantum computer, like the 1121-qubit Condor [3]. Technically, this is accomplished by employing efficient circuits that require only \(\lg n\) steps to prepare the \(|GHZ_{n}\rangle\) state (see [61]). This is particularly true for \(|GHZ_{3}\rangle\) states, being the simplest in their class. The GHZ\({}_{3}\)MQPEC protocol makes quite modest demands on the quantity of quantum resources needed. As shown in Section 6.1, the number of qubits grows linearly both in the number of millionaires \(n\) and in the number \(m\) of qubits within each quantum register, reflecting the magnitude of the numbers to be compared. This allows the protocol to seamlessly scale with respect to both the number of players and the volume of information processed. This further attests to the potential of the GHZ\({}_{3}\)MQPEC protocol for practical implementation. Another advantage of the protocol concerns its suitability for parallel as well as sequential execution. Although the execution of the quantum part of the protocol is envisioned to take place completely in parallel, it is also possible to be implemented sequentially. So, if the quantum resources are insufficient for the implementation of the protocol in one go, it is possible to partition the \(n\) of millionaires into smaller groups and process these groups sequentially, even to the point of executing the protocol serially for one millionaire at a time. Another distinguishing feature of our protocol is the existence of two third parties. Trent, featured in many previous multiparty protocols, is now accompanied by Sophia. The existence of two parties enables the simultaneous processing of all \(n\) millionaires' fortunes in one go. In addition to the possibility of either parallel or sequential execution, this protocol is flexible enough to accommodate both localized and distributed settings, a capability that stems from its inherent use of entanglement.