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Photonics Research

Entanglement and quantum coherence of hybrid entangled states

Fengyi Xu, Chenyu Qiao, Shujing Li, Meihong Wang, Xiaolong Su

Published May 13, 2025• 0 citations
Publisher

Abstract

A hybrid entangled state that involves both discrete and continuous degrees of freedom is a key resource for hybrid quantum information processing. It is essential to characterize entanglement and quantum coherence of the hybrid entangled state toward the application of it. Here, we experimentally characterize the entanglement and quantum coherence of the prepared hybrid entangled state between a polarization-encoded discrete-variable qubit and a cat-encoded wave-like continuous-variable qubit. We show that the maximum quantum coherence is obtained when the probability of the horizontal-polarization photon is 0.5, and entanglement and quantum coherence of the hybrid entangled state are robust against loss in both discrete- and continuous-variable parts. Based on the experimentally reconstructed two-mode density matrix on the bases of polarization and cat state, we obtain the logarithm negativity of 0.57 and l 1 -norm of 0.82, respectively, which confirms the entanglement and quantum coherence of the state. Our work takes a crucial step toward the application of the polarization-cat hybrid entangled state.

DOI
10.1364/prj.559233

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A hybrid entangled state that involves both discrete and continuous degrees of freedom is a key resource for hybrid quantum information processing. It is essential to characterize entanglement and quantum coherence of the hybrid entangled state toward the application of it. Here, we experimentally characterize the entanglement and quantum coherence of the prepared hybrid entangled state between a polarization-encoded discrete-variable qubit and a cat-encoded wave-like continuous-variable qubit. We show that the maximum quantum coherence is obtained when the probability of the horizontal-polarization photon is 0.5, and entanglement and quantum coherence of the hybrid entangled state are robust against loss in both discrete- and continuous-variable parts. Based on the experimentally reconstructed two-mode density matrix on the bases of polarization and cat state, we obtain the logarithm negativity of 0.57 and l 1 -norm of 0.82, respectively, which confirms the entanglement and quantum coherence of the state. Our work takes a crucial step toward the application of the polarization-cat hybrid entangled state.
In optical quantum information, one can distinguish two approaches: the discrete-variable (DV), involving single photons, for example c0|0〉 + c1|1〉, and the continuous-variable alternative (CV) encoding information into the quadrature components of the light field. In this CV approach, qubits can be implemented as superposition of coherent states of opposite phases, |cat ±〉 = |α〉 ± |−α〉, also called optical Schrodinger cat states. Combining these two approaches has recently led to a so-called optical hybrid quantum information aiming at merging the properties of both [1]. As both encodings have their own advantages and drawbacks, transferring information between them is a requirement which can be fulfill by teleportation using hybrid entanglement between particle-like qubits and wave-like qubits, i.e. entanglement of the form |0〉|α〉 + |1〉|−α〉.
Light is an irreplaceable means of communication among various quantum information processing and storage devices. Due to their different physical nature, some of these devices couple more strongly to discrete, and some to continuous degrees of freedom of a quantum optical wave. It is therefore desirable to develop a technological capability to interconvert quantum information encoded in these degrees of freedom. Here we generate and characterize an entangled state between a dual-rail (polarization-encoded) single-photon qubit and a qubit encoded as a superposition of opposite-amplitude coherent states. We furthermore demonstrate the application of this state as a resource for the interfacing of quantum information between these encodings. In particular, we show teleportation of a polarization qubit onto a freely propagating continuous-variable qubit.
Abstract Light is an irreplaceable means of communication among various quantum information processing and storage devices. Due to their different physical nature, some of these devices couple more strongly to discrete, and some to continuous degrees of freedom of a quantum optical wave. It is therefore desirable to develop a technological capability to interconvert quantum information encoded in these degrees of freedom. Here we generate and characterize an entangled state between a dual-rail (polarization-encoded) single-photon qubit and a qubit encoded as a superposition of opposite-amplitude coherent states. We furthermore demonstrate the application of this state as a resource for the interfacing of quantum information between these encodings. In particular, we show teleportation of a polarization qubit onto a freely propagating continuous-variable qubit.
Entanglement is a key resource for fundamental tests of physics and emerging quantum technologies. In quantum optics, two perspectives on entanglement coexist. In the continuous-variable framework, entanglement is understood as holding between optical modes. In contrast, discrete-variable quantum optics focuses on quantum correlations in degrees of freedom such as polarization that label fixed numbers of photons. In this paper, we show that entanglement can transcend this separation. Spontaneous parametric down-conversion inherently generates correlations in optical phase space, photon number, and labelling degrees of freedom simultaneously. In polarization, this structure is traditionally described by macroscopic Bell states. Existing witnesses, however, fail to detect the genuine hybrid entanglement of these states, which goes beyond the continuous-discrete-variable categorization. Here, we lay the groundwork for a general framework unifying continuous- and discrete-variable notions of entanglement. In particular, we derive an operational witness providing a sufficient criterion for genuine hybrid number-polarization entanglement and outline its experimental implementation. Finally, we discuss exemplary states which, together with our results on macroscopic Bell states, motivate a broader classification of genuine hybrid quantum correlations.
Quantum teleportation between polarized single-photon and phase-opposite coherent states is studied using a hybrid entangled resource and entangled coherent states. The polarized single-photon qubit represents a discrete-variable (DV) quantum system, whereas the phase-opposite coherent-state qubit constitutes a continuous-variable (CV) system. While teleportation from CV to DV can be achieved with near-unit success probability, the reverse process is usually limited to a maximum success probability of 1/21/21/2. We demonstrate that, by employing cross-Kerr nonlinearity together with passive linear optical components such as polarizing beam splitters, beam splitters, and phase shifters, almost perfect teleportation from DV to CV encodings can also be achieved.