Abstract Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs (QGs), modeled as controlled two-level quantum systems, can be utilized to generate entangled states through coherent control operations between two simple QGs. A controlled operation is defined such that the scattering behavior of one QG dynamically modifies the other. Our analysis reveals the precise conditions under which maximal entanglement or separability arises, including configurations that can be implemented via phase shifts in graph structures. Our findings demonstrate that the maximal entanglement in this system is closely related to recent results on randomized QGs. These results provide new pathways for engineering entanglement using simple QGs and suggest experimental feasibility using microwave networks.
Abstract Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs (QGs), modeled as controlled two-level quantum systems, can be utilized to generate entangled states through coherent control operations between two simple QGs. A controlled operation is defined such that the scattering behavior of one QG dynamically modifies the other. Our analysis reveals the precise conditions under which maximal entanglement or separability arises, including configurations that can be implemented via phase shifts in graph structures. Our findings demonstrate that the maximal entanglement in this system is closely related to recent results on randomized QGs. These results provide new pathways for engineering entanglement using simple QGs and suggest experimental feasibility using microwave networks.
Abstract This paper presents a theoretical framework for generating and controlling high-dimensional quantum entanglement by harnessing the scattering properties of quantum graphs (QGs). By mapping the three scattering channels of a QG onto the basis states of a quantum three-level system (qutrit), we have successfully extended the entanglement-generation protocol based on the QG from two to three dimensions. A novel triple-controlled scattering operator is introduced, which enables the conditional reconfiguration of Bob’s QG based on the scattering outcome of Alice’s. Through rigorous theoretical derivation, we establish the precise analytical conditions under which the composite system resides in either a maximally entangled or a separable state. Our findings indicate that achieving maximal entanglement requires the simultaneous satisfaction of two conditions. First, the scattering entropy of Alice’s QG must be maximal, meaning that the exit probability through each of its three channels is equal to 1 3 . Second, the three conditional output states prepared by Bob must be mutually orthogonal. Finally, we demonstrate that tunable phases can be employed to regulate the degree of entanglement actively, thereby verifying the feasibility and controllability of the proposed framework for high-dimensional quantum information processing.
The controlled generation of quantum entanglement from separable states remains a central challenge in quantum information science. Here, we investigate entanglement generation using two related control paradigms: coherent path superposition of local unitary operations and stochastic implementations of Pauli channels under coherent control. We show that entangled states belonging to the Bell, GHZ and W classes, can be deterministically generated from fully separable inputs by coherently superposing alternative sets of local unitary transformations. Conditions on the local operators for entanglement generation are derived, and the resulting states are shown to be locally unitary equivalent to standard multipartite entangled states. We further extend the analysis to noisy scenarios, where separable mixed states evolve through pairs of Pauli channels arranged in path-superposition and indefinite causal order configurations. Closed-form expressions for the output states are obtained, and entanglement is quantified using concurrence. By exploring representative channel families across their parameter space, we identify regimes where stochastic entanglement emerges, determine the associated success probabilities, and characterize trade-offs between entanglement and purity.
Graph states are intuitive representations of quantum states that are useful in quantum computing and quantum information. In this paper, we investigate the role of entanglement and local unitary equivalence in quantum computing through graph states in high-dimensional Hilbert spaces. We introduce bipartitions on the vertices sets and demonstrate separability and local unitary equivalence based on different choices of partitions. By performing the two-qubit controlled phase shift gates on various pairs of multiqubit system, one can generate a genuinely entangled graph state based on simple connected graphs. We extend 2-dimensional Hilbert spaces to higher and mixed dimensions and examine pure quantum states that cannot be separated by any bipartition. In addition, we generalize the analysis on classification of local unitary equivalence beyond the controlled-Z gates to controlled phase gates. By examining graphs constructed from bipartition graphs, we have shown that graphs with identical bipartition subgraph structures are local unitary equivalent.
Abstract Graph states are a broad family of entangled quantum states, each defined by a graph composed of edges representing the correlations between subsystems. Such states constitute versatile resources for quantum computation and quantum-enhanced measurement. Their generation and engineering require a high level of control over entanglement. Here we report on the generation of continuous-variable graph states of atomic spin ensembles, which form the nodes of the graph. We program the entanglement structure encoded in the graph edges by combining global photon-mediated interactions in an optical cavity with local spin rotations. By tuning the entanglement between two subsystems, we either localize correlations within each subsystem or enable Einstein–Podolsky–Rosen steering—a strong form of entanglement that enables the extraction of precise information from one subsystem through measurements on the other. We further engineer a four-mode square graph state, highlighting the flexibility of our approach. Our method is scalable to larger and more complex graphs, laying groundwork for measurement-based quantum computation and advanced protocols in quantum metrology.
Entanglement represents "the" key resource for several applications of quantum information processing, ranging from quantum communications to distributed quantum computing. Despite its fundamental importance, deterministic generation of maximally entangled qubits represents an on-going open problem. Here, we design a novel generation scheme exhibiting two attractive features, namely, i) deterministically generating genuinely multipartite entangled states, ii) without requiring any direct interaction between the qubits. Indeed, the only necessary condition is the possibility of coherently controlling -- according to the indefinite causal order framework -- the causal order among some unitaries acting on the qubits. Through the paper, we analyze and derive the conditions on the unitaries for deterministic generation, and we provide examples for unitaries practical implementation. We conclude the paper by discussing the scalability of the proposed scheme to higher dimensional GME states and by introducing some possible applications of the proposal for quantum networks.
This paper investigates the dynamic control of quantum states and the engineering of multi-body entanglement. The core claim centers on leveraging dynamic quantum state manipulation to construct and control multi-body entanglement, ultimately enabling effective coupling between quantum information and physical systems. This work proposes a mechanism utilizing precise control of quantum bit rotations and phases to dynamically generate and manipulate multi-body entanglement. The potential applications include advanced quantum computing and quantum sensing. The research represents a significant advancement by moving beyond the static nature of traditional quantum entanglement, offering novel opportunities for quantum technologies. We explore theoretical frameworks and potential pathways for realizing this complex entanglement structure. The key mathematical concepts used are represented as follows: |ψ⟩ denotes a quantum state, ⊗ represents the tensor product for multi-body systems, R(θ, φ) is a rotation operator, U(φ) is a phase operator, ⟨ψ|ψ⟩ represents the probability of a specific state, H(ρ) represents the Hamiltonian operator, Tr(ρ) represents the trace of a density matrix, I is the identity operator, and ε is a small parameter used in perturbation theory. The goal is to develop robust methods for creating and maintaining entanglement across multiple particles, addressing challenges related to decoherence and control fidelity. This work lays the foundation for future research into more complex entangled systems and their applications.