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arXiv:2603.12682

Optimal Continuous- to Discrete-Variable Bipartite Entanglement Conversion

Pak-Tik Fong, Ruchir Tullu, Hoi-Kwan Lau

quant-phSubmitted Mar 13, 2026• Announced Mar 16, 2026• 0 citations
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Abstract

Discrete-variable (DV) entanglement is crucial for numerous quantum applications, yet its deterministic generation in many bosonic systems remains experimentally challenging. In contrast, continuous-variable (CV) entanglement can be produced efficiently. We propose two optimal schemes for converting CV bipartite entanglement into DV entanglement using only local operations and classical communication. The first scheme extracts maximally entangled qubit pairs at the theoretically maximal rate, while the second probabilistically produces a maximally entangled qudit pair with the highest average entanglement. In both schemes, we quantify the optimal performance and identify the measurement operators required for implementation. Notably, using only a sequence of binary measurements, our approach can succeed in a finite number of measurement rounds on average, even though the CV resource is infinite-dimensional. Our schemes improve the feasibility of implementing DV-based quantum technologies on bosonic platforms.

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13 pages, 8 figures

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Discrete-variable (DV) entanglement is crucial for numerous quantum applications, yet its deterministic generation in many bosonic systems remains experimentally challenging. In contrast, continuous-variable (CV) entanglement can be produced efficiently. We propose two optimal schemes for converting CV bipartite entanglement into DV entanglement using only local operations and classical communication. The first scheme extracts maximally entangled qubit pairs at the theoretically maximal rate, while the second probabilistically produces a maximally entangled qudit pair with the highest average entanglement. In both schemes, we quantify the optimal performance and identify the measurement operators required for implementation. Notably, using only a sequence of binary measurements, our approach can succeed in a finite number of measurement rounds on average, even though the CV resource is infinite-dimensional. Our schemes improve the feasibility of implementing DV-based quantum technologies on bosonic platforms.
We show that a continuous-variable (CV) qudit can be constructed using quasiorthogonal cat states of a bosonic mode, when the phase encoded in each cat state is chosen appropriately. With the constructed CV qudit and the discrete-variable (DV) qudit encoded with Fock states, we propose an approach to generate the hybrid maximally entangled state of a CV qudit and a DV qudit by using two microwave cavities coupled to a superconducting flux qutrit. This proposal relies on the initial preparation of a superposition of Fock states of one cavity and the initial preparation of a cat state of the other cavity. After the initial state of each cavity is prepared, this proposal requires only two basic operations, i.e., the first operation employs the dispersive coupling of both cavities with the qutrit while the second operation uses the dispersive coupling of only one cavity with the qutrit. The entangled state production is deterministic and the operation time decreases as the dimensional size of each qudit increases. In addition, during the entire operation, the coupler qutrit remains in the ground state and thus decoherence from the qutrit is significantly reduced. As an example, we further discuss the experimental feasibility for generating the hybrid maximally entangled state of a DV qutrit and a CV qutrit based on circuit QED. This proposal is universal and can be extended to accomplish the same task, by using two microwave or optical cavities coupled to a natural or artificial three-level atom.
Transferring quantum information between different types of quantum hardware is crucial for integrated quantum technology. In particular, converting information between continuous-variable (CV) and discrete-variable (DV) devices enables many applications in quantum networking, quantum sensing, quantum machine learning, and quantum computing. This paper addresses the transfer of CV-encoded information between CV and DV devices. We present a resource-efficient method for encoding CV states and implementing CV gates on DV devices, as well as two measurement-based protocols for transferring CV states between CV and DV devices. The success probability of the transfer protocols depends on the measurement outcome and can be increased to near-deterministic values by adding ancillary qubits to the DV devices.
Transferring quantum information between different types of quantum hardware is crucial for integrated quantum technology. In particular, converting information between continuous variable (CV) and discrete variable (DV) devices enables many applications in quantum networking, quantum sensing, quantum machine learning, and quantum computing. This paper addresses the transfer of CV-encoded information between CV and DV devices. We present a resource-efficient method for encoding CV states and implementing CV gates on DV devices, as well as two measurement-based protocols for transferring CV states between CV and DV devices. The success probability of the transfer protocols depends on the measurement outcome and can be increased to near-deterministic values by adding ancillary qubits to the DV devices.
The study of entanglement between discrete and continuous variables is an important theoretical and experimental topic in quantum information processing, for which entanglement swapping is one of the interesting elements. Entanglement swapping allows two particles without interacting with each other in any way, to form an entangled state by the action of another pair of entangled particles. In this paper, we propose an experimentally feasible scheme to realize deterministic entanglement swapping in the hybrid system with discrete and continuous variables. The process is achieved by preparing two pairs of entangled states, each is formed by a qubit and two quasi-orthogonal coherent state elements of a cavity, performing a Bell-state analysis through nonlocal operations on the continuous variable states of the two cavities, and projecting the two qubits into a maximally entangled state. The present scheme may be applied to other physical systems sustaining such hybrid discrete and continuous forms, providing a typical paradigm for entanglement manipulation through deterministic swapping operations.
We present two strategies to enhance the dynamical entanglement transfer from continuous-variable (CV) to finite-dimensional systems by employing multiple qubits. First, we consider the entanglement transfer to a composite finite-dimensional system of many qubits simultaneously interacting with a bipartite CV field. We show that, considering realistic conditions in the generation of CV entanglement, a small number of qubits resonantly coupled to the CV system are sufficient for an almost complete dynamical transfer of the entanglement. Our analysis also sheds further light on the transition between the microscopic and macroscopic behaviors of composite finite-dimensional systems coupled to bosonic fields (like atomic clouds interacting with light). Furthermore, we present a protocol based on sequential interactions of the CV system with some ancillary qubit systems and on subsequent measurements, allowing us to probabilistically convert CV entanglement into ``almost-perfect'' Bell pairs of two qubits. Our proposals are suited for realizations in various experimental settings, ranging from cavity-QED to cavity-integrated superconducting devices.
We introduce a feasible scheme to produce high-rate long-distance entanglement that uses hybrid entanglement between continuous variables (CVs) and discrete variables (DVs). We show that hybrid entanglement can effectively remove the experimental limitations of existing CV and DV systems to produce long-range entanglement. We benchmark the resulting DV entangled states using an entanglement-based-quantum-key-distribution protocol. We show, using hybrid entangled states, that entanglement-based quantum key distribution is possible with standard telecommunication fibers for 300 km. The key idea is the use of the CV part, which can be adjusted to be robust regarding photon losses, for increasing the transmission distance, and the use of the DV part for achieving high secure key rates. Our results show that hybrid entangled states provide a clear advantage for practical generation of long-distance and high-rate entanglement that may lead to further applications in quantum information processing.