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Photonics

Deterministic Entanglement Swapping with Hybrid Discrete- and Continuous-Variable Systems

Shou‐Bang Yang, Wen Ning, Ri‐Hua Zheng, Zhen‐Biao Yang, Shi‐Biao Zheng

Published May 25, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.3390/photonics9060368

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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.
By coherently combining advantages while largely avoiding limitations of two mainstream platforms, optical hybrid entanglement involving both discrete and continuous variables has recently garnered widespread attention and emerged as a promising idea for building heterogenous quantum networks. In contrast to previous results, here we propose a new scheme to remotely generate hybrid entanglement between discrete polarization and continuous quadrature optical qubits heralded by two-photon Bell-state measurement. As a novel nonclassical light resource, we further use it to discuss two examples of ways—entanglement swapping and quantum teleportation—in which quantum information processing and communications could make use of this hybrid technique.
We experimentally realize "hybrid" entanglement swapping between discrete-variable (DV) and continuous-variable (CV) optical systems. DV two-mode entanglement as obtainable from a single photon split at a beam splitter is robustly transferred by means of efficient CV entanglement and operations, using sources of squeezed light and homodyne detections. The DV entanglement after the swapping is verified without postselection by the logarithmic negativity of up to 0.28±0.01. Furthermore, our analysis shows that the optimally transferred state can be postselected into a highly entangled state that violates a Clauser-Horne-Shimony-Holt inequality by more than 4 standard deviations, and thus it may serve as a resource for quantum teleportation and quantum cryptography.
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.
Hybrid entangled states generated, e.g., in a trapped-ion or atom-cavity system, have exactly one ebit of entanglement, but are not maximally entangled. We demonstrate this by showing that they violate, but, in general, not maximally, Bell's inequality due to Clauser, Horne, Shimony, and Holt [Phys. Rev. Lett. 23, 880 (1969)]. These states are interesting in that they exhibit the entanglement between two distinct degrees of freedom (one is discrete and another is continuous). We then demonstrate these entangled states as a valuable resource in quantum-information processing including quantum teleportation, entanglement swapping and quantum computation with ``parity qubits.'' Our work establishes an interesting link between quantum-information protocols of discrete and continuous variables.
Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is deterministically transferred to another qubit that has never interacted with it. We further realize delayed-choice entanglement swapping, showing whether two qubits previously behaved as in an entangled state or as in a separable state is determined by a later choice of the type of measurement on their partners. This is the first demonstration of entanglement-separability duality in a deterministic way.
Entanglement swapping, which is a core component of quantum network and an important platform for testing the foundation of quantum mechanics, can enable the entangling of two independent particles without direct interaction both in discrete variable and continuous variable systems. Conventionally, the realization of entanglement swapping relies on the Bell-state measurement. In particular, for entanglement swapping in continuous variable regime, such Bell-state measurement involves the optic-electro and electro-optic conversion, which limits the applications of the entanglement swapping for constructing broadband quantum network. In this Letter, we propose and demonstrate a measurement-free all-optical entanglement swapping. In our scheme, a high-gain parametric amplifier based on the four-wave mixing process is exploited to realize the function of Bell-state measurement without detection, which avoids the introduction of the optic-electro and electro-optic conversion. Our results provide an all-optical paradigm for implementing entanglement swapping and pave the way to construct a measurement-free all-optical broadband quantum network.