Motivated by the Bose et al.-Matletto-Vedral (BMV) proposal for detecting quantum superposition of spacetime geometries, we study a toy model of a quantum entanglement generation between two spins (qubits) mediated by a relativistic free scalar field. After time evolution, spin correlation is generated through the interactions with the field. Because of the associated particle creation into an open system, the quantum state of spins is partially decohered. In this paper, we give a comprehensive study of the model based on the closed time path formalism, focusing on relativistic causality and quantum mechanical complementarity. We calculate various quantities such as spin correlations, entanglement entropies, mutual information and negativity, and study their behaviors in various limiting situations. In particular, we calculate the mutual information of the two spins and compare it with spin correlation functions. In some cases, its inequality relation improves the trade-off relation between the fringe visibility and the distinguishability (which-way information) by giving a stronger upper bound on the visibility. We also discuss why no quantum entanglement can be generated unless both spins are causally affected by one another while spin correlations are generated.
Motivated by the Bose et al.-Matletto-Vedral (BMV) proposal for detecting quantum superposition of spacetime geometries, we study a toy model of a quantum entanglement generation between two spins (qubits) mediated by a relativistic free scalar field. After time evolution, spin correlation is generated through the interactions with the field. Because of the associated particle creation into an open system, the quantum state of spins is partially decohered. In this paper, we give a comprehensive study of the model based on the closed time path formalism, focusing on relativistic causality and quantum mechanical complementarity. We calculate various quantities such as spin correlations, entanglement entropies, mutual information and negativity, and study their behaviors in various limiting situations. In particular, we calculate the mutual information of the two spins and compare it with spin correlation functions. In some cases, its inequality relation improves the trade-off relation between the fringe visibility and the distinguishability (which-way information) by giving a stronger upper bound on the visibility. We also discuss why no quantum entanglement can be generated unless both spins are causally affected by one another while spin correlations are generated.
Entanglement generation by Newtonian gravitational potential between objects has been widely discussed to reveal the quantum nature of gravity. In this paper, we perform a quantum field theoretical analysis of a slightly modified version of the gedanken experiment by Mari and co-workers [A. Mari et al., Sci. Rep. 6, 22777 (2016).]. We show that decoherence due to the presence of a detector propagates with the speed of light in terms of a retarded Green's function, as it should be consistent with causality of relativistic field theories. The quantum nature of fields, such as quantum fluctuations or emission of gravitons expressed in terms of the Keldysh Green's function also play important roles in the mechanism of decoherence due to on-shell particle creation. We also discuss the trade-off relation between the visibility of the interference and the distinguishability of the measurement, known as the particle-wave duality, in our setup.
A scheme to generate shared tripartite entangled states, with two-trapped atoms in a cavity held by Alice (qubits A1 and A2) entangled to a single-trapped atom in a remote laboratory owned by Bob (B), is proposed. The entanglement is generated through interaction of trapped atoms with two-mode squeezed light shared by the two cavities. The proposed scheme is an extension of the proposal of Son et al. [J. Mod. Opt. 49, 1739 (2002)], where the possibility of entangling two remote qubits using a bipartite continuous variable state was examined. While the global negativity detects the free entanglement of the three atom mixed state, the bound entanglement is detected by the negativity calculated from pure state decomposition of the state operator. The partial negativities calculated by selective partial transposition of the three atom mixed state detect the pairwise entanglement of qubit pairs A1B, A2B, and A1A2. The entanglement of three atoms is found to be W-like, no Greenberger-Horne-Zeilinger-like quantum correlations being generated.
We consider Unruh–Wald qubit detector model adopted for the far future region of an exactly solvable 1+1 dimensional scalar field theory in a toy model of Robertson–Walker expanding spacetime. It is shown that the expansion of the spacetime in its history enhances the decoherence of the qubit coupled with a scalar field. Moreover, we consider two entangled qubits, each locally coupled with a scalar field. The expansion of the spacetime in its history degrades the entanglement between the qubits, and it can lead to entanglement’s sudden death if the initial entanglement is small enough. The details depend on the parameters characterizing the expansion of the spacetime. This work, on a toy model, suggests that the history of the spacetime might be probed through the coherent and entanglement behavior of the future detectors of quantum fields. In the present toy model, the two cosmological parameters can be determined from the quantum informational quantities of the detectors.
Coherence and complementarity are two important themes in quantum mechanics, which have been widely and thoroughly investigated. Recently, with the rapid development of quantum information theory, various measures have been introduced for quantitatively studying the coherence and complementarity. However, most of these studies are independent of each other in that they focus on only one theme, for example, the wave-particle duality and Heisenberg uncertainty principle are usually regarded as manifestation of Bohr’s complementary principle, while coherence is a quantum feature closely related to quantum superposition. During the past few years, there has been a flurry of research interest in the study of quantum coherence from the quantum resource-theoretic point of view. In this paper, we establish two information conservation relations and employ them to characterize complementarity and quantum coherence. As an illustration of the main results, we discuss these two themes in the Mach-Zehnder interferometer. Our study reveals that these two quantum themes are closely related to each other. Our main results are listed as follows. Firstly, we establish two information conservation relations, one is based on " Bures distance versus fidelity” and the other based on " symmetry versus asymmetry”. Then we employ these information conservation relations to investigate coherence and complementarity. Specifically, we provide an explanation of the " Bures distance versus fidelity” trade-off relation from the information conservation perspective, establish the link between the information conservation relation and wave-particle duality, and derive the famous Englert inequality concerning " fringe visibility versus path distinguishability” from the information conservation relation. Furthermore, in the general framework of state-channel interaction, we derive " symmetry versus asymmetry” trade-off relation and explain it as an information conservation relation, reveal its intrinsic relations with coherence and complementarity. Lastly, we demonstrate that the two information conservation relations are closely interrelated, and we also discuss the coherence, decoherence and complementarity in the Mach-Zehnder interferometer, explicitly, we reveal that the Bures distance can be regarded as a lower bound of the asymmetry of state-channel interaction while fidelity is an upper bound of the symmetry of state-channel interaction. We expect that our information conservation relation can provide a unified framework for the study of coherence and complementarity.
The generation of entangled states and their degree of entanglement are studied in a relativistic formulation for the case of two interacting spin-1/2 charged particles. In the realm of quantum electrodynamics, we revisit the interaction that produces entanglement between the spin components of covariant Dirac spinors describing the two particles. In this way, we derive the relativistic version of the spin-spin interaction, widely used in the nonrelativistic regime. Following this consistent approach, the relativistic invariance of the generated entanglement is discussed.
Due to the rapid development of research in the field of quantum physics and quantum information over the past decades, the need to study physical models that can effectively implement quantum computing has increased. An integral part of such models is the environment, which, on the one hand, leads to decoherence in the system, and on the other hand, generates interaction between spins, which in turn allows for the induction of entanglement, which is an integral part of many quantum algorithms. Therefore, it is essential to investigate the impact of the environment on the behavior of quantum systems, enabling the effective implementation of quantum information devices. Here, we consider the time evolution of two spins generated by the interaction through a bosonic environment. The behavior of negativity as a measure of entanglement between spins is studied for different models of environment. As a result, conditions on the parameters of the environment are obtained to achieve the maximum values of entanglement between spins. In this case, environmental models were obtained that minimize the decoherence of the system while maximizing its entanglement. It became possible to derive an effective unitary operator describing the corresponding evolution, since the influence of decoherence was negligibly small.