arXiv subjects

Ahmad Nawaz

Publications and source records attributed to Ahmad Nawaz.

13 recordsLinked to original sources

arXiv2025

The Dynamics of Cosmic Evolution: Insights from Bouncing Cosmology

The primary aim of this work is to explore feasible bouncing cosmological solutions in the framework of $f(\mathcal{Q}, \mathcal{C})$ gravity, where $\mathcal{Q}$ denotes non-metricity and $\mathcal{C}$ indicates the boundary term. To achieve this, we analyze the dynamics of a Bianchi type-I spacetime with perfect fluid distribution. We consider various functional forms of $f(\mathcal{Q,C})$ theory to assess how this modified gravity framework influences cosmic evolution. Additionally, we examine the dynamics of different cosmological parameters to explore non-singular bounce solutions. We also use linear perturbation to study the stability analysis. Our findings reveal the breach of the null energy conditions, which is required for the existence of viable bounce solutions. The equation of state parameter demonstrates either a quintessence phase or a phantom regime of the universe, demonstrating that the cosmos is undergoing accelerating expansion. This gravitational framework presents a promising alternative to the standard cosmological model, presenting an innovative viewpoint on gravitational interactions and the dynamics of the early universe.

gr-qc↗

arXiv2013

Prisoners' Dilemma in Presence of Collective Dephasing

We quantize prisoner dilemma in presence of collective dephasing with dephasing rate $γ$. It is shown that for two parameters set of strategies $Q\otimes Q$ is Nash equilibrium below a cut-off value of time. Beyond this cut-off it bifurcates into two new Nash equilibria $Q\otimes D$ and $D\otimes Q$. Furthermore for maximum value of decoherence \ $C\otimes D$ and $D\otimes C$ also become Nash equilibria. At this stage the game has four Nash equilibria. On the other hand for three parameters set of strategies there is no pure strategy Nash equilibrium however there is mixed strategy (non unique) Nash equilibrium that is not affected by collective dephasing..

quant-ph↗

arXiv2013

Werner-like States and Strategic Form of Quantum Games

We quantize prisoners dilemma, chicken game and battle of sexes to explore the effect of quantization on their strategic form. The games start with Werner-like state as an initial state. We show that for the measurement in entangled basis the strategic forms of these games remain unaffected by quantization. On the other hand when measurement is performed in product basis then these games could not retain their strategic forms.

quant-ph↗

arXiv2013

The strategic form of quantum prisoners' dilemma

In its normal form prisoners' dilemma (PD) is represented by a payoff matrix showing players strategies and payoffs. To obtain distinguishing trait and strategic form of PD certain constraints are imposed on the elements of its payoff matrix. We quantize PD by generalized quantization scheme to analyze its strategic behavior in quantum domain. The game starts with general entangled state of the form $\left}ψ\right\rangle =\cos\fracξ% {2}\left|00\right\rangle +i\sin\fracξ{2}\left|11\right\rangle $ and the measurement for payoffs is performed in entangled and product bases. We show that for both measurements there exist respective cutoff values of entanglement of initial quantum state up to which strategic form of game remains intact. Beyond these cutoffs the quantized PD behaves like chicken game up to another cutoff value. For the measurement in entangled basis the dilemma is resolved for\ $\sinξ>\frac{1}{7}$ with $Q\otimes Q$ as a NE but the quantized game behaves like PD when $\sinξ>\frac{1}{3}$; whereas in the range $\frac{1}{7}<\sinξ<\frac{1}{3}$ it behaves like chicken game (CG)\ with $Q\otimes Q$ as a NE. For the measurement in product basis the quantized PD behaves like classical PD for $\sin^{2}\fracξ{2}<\frac{1}{3}$ with $D\otimes D$ as a NE. In region $\frac{1}{3}<\sin^{2}\fracξ{2}% <\frac{3}{7}$ the quantized PD behaves like classical CG with $C\otimes D$ and $D\otimes C$ as NE.

quant-ph↗

arXiv2011

Quantum State Tomography and Quantum Games

We develop a technique for single qubit quantum state tomography using the mathematical setup of generalized quantization scheme for games. In our technique Alice sends an unknown pure quantum state to Bob who appends it with |0><0| and then applies the unitary operators on the appended quantum state and finds the payoffs for Alice and himself. It is shown that for a particular set of unitary operators these elements become equal to Stokes parameters for an unknown quantum state. In this way an unknown quantum state can be measured and reconstructed. Strictly speaking this technique is not a game as no strategic competitions are involved.

quant-ph↗

arXiv2010

The Generalized Quantization Schemes for Games and its Application to Quantum Information

Theory of quantum games is relatively new to the literature and its applications to various areas of research are being explored. It is a novel interpretation of strategies and decisions in quantum domain. In the earlier work on quantum games considerable attention was given to the resolution of dilemmas present in corresponding classical games. Two separate quantum schemes were presented by Eisert et al. and Marinatto and Weber to resolve dilemmas in Prisoners' Dilemma and Battle of Sexes games respectively. However for the latter scheme it was argued that dilemma was not resolved. We have modified the quantization scheme of Marinatto and Weber to resolve the dilemma. We have developed a generalized quantization scheme for two person non-zero sum games which reduces to the existing schemes under certain conditions. Applications of this generalized quantization scheme to quantum information theory are studied. Measurement being ubiquitous in quantum mechanics can not be ignored in quantum games. With the help of generalized quantization scheme we have analyzed the effects of measurement on quantum games. Qubits are the important elements for playing quantum games and are generally prone to decoherence due to their interactions with environment. An analysis of quantum games in presence of quantum correlated noise is performed in the context of generalized quantization scheme. Quantum key distribution is one of the key issues of quantum information theory for the purpose of secure communication. Using mathematical framework of generalized quantization scheme we have proposed a protocol for quantum key distribution and a technique for quantum state tomography.

quant-ph↗

arXiv2010

Quantum Games and Quantum Discord

We quantize prisoners dilemma and chicken game by our generalized quantization scheme to explore the role of quantum discord in quantum games. In order to establish this connection we use Werner-like state as an initial state of the game. In this quantization scheme measurement can be performed in entangled as well as in product basis. For the measurement in entangled basis the dilemma in both the games can be resolved by separable states with non-zero quantum discord. Similarly for product basis measurement the payoffs are quantum mechanical only for nonzero values of quantum discord.

quant-ph↗

arXiv2010

Evolutionarily Stable Strategies in Quantum Hawk-Dove Game

We quantized the Hawk-Dove game by using the most general form of a pure initial state to investigate the existence of pure and mixed Evolutionarily Stable Strategies (ESS). An example is considered to draw a comparison between classical and quantum version of the game. Our choice of most general initial quantum state enables us to make the game symmetric or asymmetric. We show that for a particular set of game parameters where there exist only mixed ESS in the classical version of the game, however, quantization allows even a pure strategy to be an ESS for symmetric game in addition to ixed ESS. On the other hand only pure strategy ESS can exist for asymmetric quantum version of the Hawk-Dove game.

quant-ph↗

arXiv2008

The effect of quantum memory on quantum games

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.

quant-ph↗

arXiv2006

Quantum Games with Correlated Noise

We analyze quantum game with correlated noise through generalized quantization scheme. Four different combinations on the basis of entanglement of initial quantum state and the measurement basis are analyzed. It is shown that the advantage that a quantum player can get by exploiting quantum strategies is only valid when both the initial quantum state and the measurement basis are in entangled form. Furthermore, it is shown that for maximum correlation the effects of decoherence diminish and it behaves as a noiseless game.

quant-ph↗

arXiv2006

The Role of Measurement in Quantum Games

The game of Prisoner Dilemma is analyzed to study the role of measurement basis in quantum games. Four different types of payoffs for quantum games are identified on the basis of different combinations of initial state and measurement basis. A relation among these different payoffs is established.

quant-ph↗

arXiv2004

Generalized Quantization Scheme for Two-Person Non-Zero-Sum Games

We have proposed a generalized quantization scheme for non-zero sum games which can be reduced to two existing quantization schemes under appropriate set of parameters. Some other important situations are identified which are not apparent in the exiting two quantizations schemes.

quant-ph↗

arXiv2004

Dilemma and Quantum Battle of Sexes

We analysed quantum version of the game battle of sexes using a general initial quantum state. For a particular choice of initial entangled quantum state it is shown that the classical dilemma of the battle of sexes can be resolved and a unique solution of the game can be obtained.

quant-ph↗