The Prisoner’s Dilemma game (PDG) is one of the simple test-beds for the probabilistic nature of the human decision-making process. Behavioral experiments have been conducted on this game for decades and show a violation of the so-called sure thing principle, a key principle in the rational theory of decision. Quantum probabilistic models can explain this violation as a second-order interference effect, which cannot be accounted for by classical probability theory. Here, we adopt the framework of generalized probabilistic theories and approach this explanation from the viewpoint of quantum information theory to identify the source of the interference. In particular, we reformulate one of the existing quantum probabilistic models using density matrix formalism and consider different amounts of classical and quantum uncertainties for one player’s prediction about another player’s action in PDG. This enables us to demonstrate that what makes possible the explanation of the violation is the presence of quantum coherence in the player’s initial prediction and its conversion to probabilities during the dynamics. Moreover, we discuss the role of other quantum information-theoretical quantities, such as quantum entanglement, in the decision-making process. Finally, we propose a three-choice extension of the PDG to compare the predictive powers of quantum probability theory and a more general probabilistic theory that includes it as a particular case and exhibits third-order interference.
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We investigate the influence of geometry on the preservation of quantum coherence in spin clusters subjected to a thermal environment. Assuming weak inter-spin coupling, we explore the various buffer network configurations that can be embedded in a plane. Our findings reveal that the connectivity of the buffer network is crucial in determining the preservation duration of quantum coherence in an individual central spin. Specifically, we observe that the maximal planar graph yields the longest preservation time for a given number of buffer spins. Interestingly, our results demonstrate that the preservation time does not consistently increase with an increasing number of buffer spins. Employing a quantum master equation in our simulations, we further demonstrate that a tetrahedral geometry comprising a four-spin buffer network provides optimal protection against environmental effects.
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The field of quantum resource theory (QRT) has emerged as an invaluable framework for the examination of small and strongly correlated quantum systems, surpassing the boundaries imposed by traditional statistical treatments. The fundamental objective of general QRTs is to characterize these systems by precisely quantifying the level of control attainable to an experimenter. In this review article, we refrain from providing an exhaustive summary of the extensive literature on QRT. Rather, our focus centers on a specific subliterature founded upon the theory of majorization. The primary aim is to augment our comprehension of genuine quantum phenomena manifested across diverse technological applications and incite investigations into novel resource theories encompassing multiple types of resources. Consequently, we emphasize the underlying similarities shared by various resources, including bipartite quantum entanglement, quantum coherence, and superposition, alongside informational, thermal, and generalized nonequilibrium resources.
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The quantum superposition principle has been extensively utilized in the quantum mechanical description of bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of near-exact electronic wavefunctions. On the other hand, its existence in composite systems may give rise to nonclassical correlations that are regarded as a resource in quantum technologies. Here, we approach the electronic ground states of three prototypical molecules in the light of the framework set by fermionic information theory. By introducing the notion of orbital discord, we additively decompose the pairwise orbital correlations into their classical and quantum parts in the presence of superselection rules. We observe that quantum orbital correlations can be stronger than classical orbital correlations though not often. Moreover, quantum orbital correlations can survive even in the absence of orbital entanglement depending on the symmetries of the constituent orbitals. Finally, we demonstrate that orbital entanglement would be underestimated if the orbital density matrices were treated as qubit states.
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We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon- electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn- Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular entanglement between the vibrational phonon modes, and present analytical explanations using a single privileged Jahn-Teller mode picture. Furthermore, spin-orbit entanglement or quantum correlations between electronic and vibrational degrees of freedom are examined. We conclude by discussing experimental feasibility to detect such quantum correlations, considering the dephasing and decoherence in state-of-the-art superconducting two-level systems (qubits).
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The role of quantum coherence and correlations in heat flow and equilibration is investigated by exploring the Rayleigh’s dynamical problem to equilibration in the quantum regime and following Onsager’s approach to thermoelectricity. Specifically, we consider a qubit bombarded by two-qubit projectiles from a side. For arbitrary collision times and initial states, we develop the master equation for sequential and collective collisions. By deriving the Fokker-Planck equation out of the master equation, we identify the quantum version of the Rayleigh’s heat conduction equation. We find that quantum discord and entanglement shared between the projectiles can contribute to genuine heat flow only when they are associated with so-called heat-exchange coherences. Analogous to Onsager’s use of Rayleigh’s principle of least dissipation of energy, we use the entropy production rate to identify the coherence current. Both coherence and heat flows can be written in the form of quantum Onsager relations, from which we predict coherent Peltier and coherent Seebeck effects. The effects can be optimized by the collision times and collectivity. Finally, we discuss some of the possible experimental realizations and technological applications of the thermocoherent phenomena in different platforms.
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Several experimental and theoretical studies report instances of concerted or correlated multiple proton tunnelling in solid phases of water. Here, we construct a pseudo-spin model for the quantum motion of protons in a hexameric H2O ring and extend it to open system dynamics that takes environmental effects into account in the form of O–H stretch vibrations. We approach the problem of correlations in tunnelling using quantum information theory in a departure from previous studies. Our formalism enables us to quantify the coherent proton mobility around the hexagonal ring by one of the principal measures of coherence, the l1 norm of coherence. The nature of the pairwise pseudo-spin correlations underlying the overall mobility is further investigated within this formalism. We show that the classical correlations of the individual quantum tunnelling events in long-time limit is sufficient to capture the behaviour of coherent proton mobility observed in low-temperature experiments. We conclude that long-range intra-ring interactions do not appear to be a necessary condition for correlated proton tunnelling in water ice.
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The role of proton tunnelling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyses the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.
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Quantum tunneling events occurring through biochemical bonds are capable of generating quantum correlations between bonded systems, which in turn makes the conventional second law of thermodynamics approach insufficient to investigate these systems. This means that the utilization of these correlations in their biological functions could give an evolutionary advantage to biomolecules to an extent beyond the predictions of molecular biology that are generally based on the second law in its standard form. To explore this possibility, we first compare the tunneling assisted quantum entanglement shared in the ground states of covalent and hydrogen bonds. Only the latter appears to be useful from a quantum information point of view. Also, significant amounts of quantum entanglement can be found in the thermal state of hydrogen bond. Then, we focus on an illustrative example of ligand binding in which a receptor protein or an enzyme is restricted to recognize its ligands using the same set of proton-acceptors and donors residing on its binding site. In particular, we show that such a biomolecule can discriminate between 3n−1 agonist ligands if it uses the entanglement shared in n intermolecular hydrogen bonds as a resource in molecular recognition. Finally, we consider the molecular recognition events encountered in both the contemporary genetic machinery and its hypothetical primordial ancestor in pre-DNA world, and discuss whether there may have been a place for the utilization of quantum entanglement in the evolutionary history of this system.
Read More: the source / arXiv