In quantum mechanics, neither deletion nor cloning are possible. The second law of thermodynamics also applies: in a closed system, entropy cannot be decreased. The second law can be expressed even more forcefully: eigenvalues of density matrices do not change as a result of quantum evolution. And this is the principle of information conservation. We raise the expression of the no-deleting theorem to the level of a principle in the following section. The no-deleting principle is then demonstrated to be contained in the second law of thermodynamics. Since the system is closed, the fall in entropy is a violation of thermodynamics' second law. In other words, the no-deletion principle is implied by the second law of thermodynamics.

The integration of quantum mechanics and classical game theory led to the development of quantum game theory in the works of Eisert et al. Game theory is a mathematical framework that analyses the decision making involved in real-life competitive scenarios. With this theory, one can determine a player's optimum reaction and the related payoff, also known as the game's outcome. A game may be defined as any real-life event that has the following components: participants, strategy, and a set of rules. Now in the quantum domain of game theory we have one more component known as entanglement which is a weird quantum correlation between the microscopic particles of a system. One may observe the breadth of game theory in other disciplines, including economics, biology, and so on.

The competitive market situation that exists between various manufacturing enterprises is referred to as oligopoly in economics, while duopoly games are simpler to deal with. It is found that given an appropriate choice of entangling operators, follower advantage game can be switched to a leader advantage game in the quantum form of the noisy duopoly games (Leader follower game). A new quantization method known as the modified EWL scheme is used to study the quantum Stackelberg-Bertrand duopoly game, also known as the follower advantage game. The distinguishing feature of this scheme is that it offers a wide range of two-qubit entangling operators that are not otherwise available in EWL and MW scheme. Applying this scheme, it is found that maximum noise eliminates the role of entangling operators when the communications are highly decohered in the case of amplitude and phase damping. In other words, the quantum correlation that is brought forth by quantum entanglement is killed by the maximum noise.

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