We consider the effect of a thermal bath on quantum correlations induced by the gravitational interaction in the weak field limit between two massive cat states, called gravitational cat (gravcat) states. The main goal of this paper is to provide a good understanding of the effects of temperature and several parameters in the entanglement (measured by the concurrence) and quantum coherence (measured by the l1-norm that is defined from the minimal distance between the quantum state and the set of incoherent states) which are derived from the thermal quantum density operator. Our results show that the thermal concurrence and l1-norm can be significantly optimized by increasing the masses or decreasing the distance between them. We investigate and discuss the behavior of these quantities under temperature variations in different regimes, including some that are expected to be experimentally feasible in the future. In particular, we observe that thermal fluctuations raise non-entangled quantum correlations when entanglement suddenly drops.
We consider the effect of a thermal bath on quantum correlations induced by the gravitational interaction in the weak field limit between two massive cat states, called gravitational cat (gravcat) states. The main goal of this paper is to provide a good understanding of the effects of temperature and several parameters in the entanglement (measured by the concurrence) and quantum coherence (measured by the l1-norm that is defined from the minimal distance between the quantum state and the set of incoherent states) which are derived from the thermal quantum density operator. Our results show that the thermal concurrence and l1-norm can be significantly optimized by increasing the masses or decreasing the distance between them. We investigate and discuss the behavior of these quantities under temperature variations in different regimes, including some that are expected to be experimentally feasible in the future. In particular, we observe that thermal fluctuations raise non-entangled quantum correlations when entanglement suddenly drops.
In this article, we investigate the hierarchy of quantum correlations between two gravitational cats states (modeled by two qubits). We use concurrence to quantify the entanglement between the two gravitational cat states. Quantum steering is employed to measure the steerabilities. We consider geometric quantum discord to quantify quantum correlations beyond entanglement. We show that the concurrence persists even when steerability is lost under thermal effects. We also show that the temperature influences the degree of quantum correlations between the two gravitational cat states. Besides, when the energy difference between the ground state and the first excited level becomes significant, the states become separable.
We explore the quantum features of two gravitational cats (gravcats) modeled by two qubits, focusing on quantum steerability, concurrence, and geometric quantum discord under varying conditions of gravitational interaction strength, temperature, and excitation energy. We first analyze the system without dephasing effects, revealing that two-way quantum steering occurs at lower temperatures and higher gravitational interaction strengths. As temperature increases, thermal noise reduces steerability, though gravitational effects remain significant, indicating a non-monotonic behavior dependent on energy and mass scales. Furthermore, quantum correlations exhibit a hierarchy, with geometric quantum discord persisting even when steering and entanglement vanish. We then explore the impact of environmental dephasing and classical correlations on the system's dynamics. Our findings demonstrate that classical correlations in correlated dephasing channels can protect quantum resources, enhancing their stability in both Markovian and non-Markovian regimes. This work highlights the intricate interplay between gravitational interactions, thermal effects, and environmental noise in preserving quantum resources.
We study the distribution of quantum correlations and basis-independent coherence in a pair of massive particles confined in a double-well potential and coupled through their mutual Newtonian gravitational interaction. Non-classical correlations are characterized using Bures distance of entanglement and quantum discord, while coherence is quantified through the square root of the quantum Jensen--Shannon divergence (QJSD) from the maximally mixed state, yielding a measure that is invariant under arbitrary unitary transformations and is therefore genuinely basis-independent. The total coherence CT decomposes into two operationally distinct contributions: the collective coherence CC, which captures quantum correlations between the two subsystems, and the localized coherence CL, which captures the intrinsic quantum coherence of each individual subsystem. We analyze how temperature T, the gravitational coupling Δ, and the single-particle energy scale w govern the redistribution of coherence between its collective and localized components. Our results show that CL is more robust against thermal fluctuations than CC, and that increasing Δ preferentially enhances collective coherence by strengthening gravitationally induced inter-particle correlations.
Gravitationally induced entanglement has been proposed as a probe of the quantum nature of gravity. This work analyzes a system of two particles in harmonic traps interacting only through gravity, considering thermal and two-mode squeezed initial states. For thermal states, a maximum temperature is identified above which entanglement cannot be generated, and for fixed system parameters an optimal trap frequency that maximizes the logarithmic negativity is found. Squeezing the initial state does not further enhance the entanglement generation, but increases the temperature range over which it can be observed. Extending the analysis to general Gaussian states, an upper bound on the achievable entanglement is derived and shown to be saturated, for example, by ground and squeezed states. The results show that the amount of entanglement generated in this setup is extremely small, highlighting the experimental challenges of observing gravitationally induced quantum effects.
Abstract We extend our earlier work [1] on probing a gravitational cat state (gravcat) to the quantum superposition of two gravcats in an exemplary model and in Bose–Einstein condensates (BEC). In addition to its basic theoretical values in gravitational quantum physics and macroscopic quantum phenomena, this investigation can provide some theoretical support to experimental proposals for measuring gravity-induced entanglement and the quantum nature of perturbative gravity. In the first part we consider cat states generated by double-well potentials. A pair of gravcats, each approximated as a two-level system, is characterized by gravity - induced Rabi oscillations , and by gravity - induced entanglement of its energy eigenstates. In the second part we turn to a (non-relativistic) quantum field theory description and derive a gravitational Gross – Pitaevsky equation for gravcats formed in BEC. Using a mathematical analogy to quantum rotors, we explore the properties of the two-gravcat system for BECs, its physical consequences and observational possibilities. Finally we discuss our results in comparison to predictions of alternative quantum theories, and we explain their implications.
We investigate the multiparameter quantum estimation and quantum thermodynamics properties of a gravitational cat state (gravcat) system composed of two interacting massive particles confined in double-well potentials. The system is described by an effective Hamiltonian involving the energy splitting parameter ω and the gravitational coupling strength γ, while the interaction with a thermal environment is modeled through a Gibbs thermal state. Within the framework of quantum parameter estimation theory, we employ the quantum Fisher information matrix (QFIM) to analyze the precision limits for estimating the three fundamental parameters of the model, namely the gravitational coupling γ, the energy splitting ω, and the temperature T. Utilizing the symmetric logarithmic derivative (SLD) formalism within the QFIM framework, we derive the analytical expressions of the estimation bounds and evaluate the corresponding minimal variances associated with the quantum Cramér-Rao bound. Both simultaneous and individual estimation strategies are investigated, and their performances are compared in different parameter regimes. Our results reveal the existence of optimal estimation regions where the precision is significantly enhanced and show that the relative efficiency of the estimation schemes strongly depends on the interaction strength, the energy gap, and the thermal environment. In addition, the thermodynamic behavior of the system is analyzed within the framework of a quantum Stirling cycle. The internal energy, entropy, heat exchanges, and work production are examined, allowing us to evaluate the efficiency of the gravcat-based quantum heat engine. The obtained results highlight the interplay between quantum metrology and quantum thermodynamics.