Transfer of Quantum Entanglement

• Transfer of Quantum Entanglement (TQE) is the process of faithfully delivering non-classical correlations across complex channels via diverse protocols and state-mapping techniques.
• It encompasses light–matter mappings, photonic interconversion, and spin-chain mechanisms that employ beam-splitter interactions and Hamiltonian dynamics to preserve entanglement.
• Practical implementations demonstrate high efficiency and fidelity using deterministic, heralded, counterfactual, and multipartite approaches in quantum memories, spin systems, and superconducting arrays.

Searching arXiv for the specified TQE papers and closely related work to ground the article in current arXiv records. arXiv search query: "Transfer of Quantum Entanglement (Cao et al., 2020, Huang et al., 2021, Valencia et al., 2019, Su et al., 2016, Yan et al., 2017, Roy et al., 2024, Wang et al., 7 Jun 2026)"

Transfer of Quantum Entanglement (TQE) denotes the faithful delivery of non-classical correlations—i.e. entanglement—between two parties when one or both photons of an entangled pair traverse a noisy, complex channel, and, in spin-dynamical settings, the process by which an entangled pair of qubits relinquishes its quantum correlations to a different pair through coherent Hamiltonian evolution (Valencia et al., 2019, Karst et al., 2024). In current arXiv literature, the term covers reversible light–matter mapping in quantum memories, two-way conversion between photonic degrees of freedom, state and entanglement transport in spin chains and superconducting arrays, cavity- and coupler-mediated multipartite transfer, counterfactual and waveguide-QED protocols, and measurement-induced transfer from a nonlocal photon to non-Gaussian continuous-variable states (Cao et al., 2020, Huang et al., 2021, Banchi et al., 2011, Li et al., 2018, Podoshvedov et al., 22 Sep 2025).

1. Scope and conceptual variants

TQE is not restricted to a single operational primitive. In reversible memory protocols, the objective is to map an optical entangled state into a collective spin excitation and later retrieve it with high efficiency and preserved nonclassicality. In photonic interfaces, the goal is coherent transfer between degrees of freedom, such as time–energy and orbital angular momentum (OAM), while preserving the entangled state. In spin and superconducting systems, the emphasis is often on coherent propagation, mirror transfer, or parity-dependent nonlocal phases generated by nearest-neighbour couplings. In open systems, TQE may refer to transient concurrence enhancement, steady-state entanglement under pumping, or entanglement preservation in the presence of dissipation and mode mixing (Cao et al., 2020, Huang et al., 2021, Roy et al., 2024, Song et al., 2014, Li et al., 2018).

The literature also distinguishes deterministic, heralded, probabilistic, and counterfactual regimes. Deterministic multipartite transfer appears in continuous-variable (CV) light–matter interfaces and in engineered chain dynamics. Heralded protocols appear in single-photon storage and in photon-number-conditioned DV-to-CV transfer. Counterfactual transfer uses nested interferometers so that no photon or matter carrier traverses the channel; if one did, the protocol would fail. This suggests that “transfer” should be read operationally: the entanglement resource is relocated, re-encoded, or re-expressed, but the physical mechanism varies sharply across platforms (Yan et al., 2017, Podoshvedov et al., 22 Sep 2025, Guo et al., 2014).

2. Dynamical frameworks and state-mapping formalisms

A recurring structure in TQE is a beam-splitter-type interaction. In EIT-based memories the signal field and a classical control field couple three atomic levels $|g\rangle, |e\rangle, |s\rangle$, with interaction Hamiltonian

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$

Under adiabatic EIT conditions, the dark-state polariton

$$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$

interpolates between photonic and collective-spin character as $\Omega(t)$ is varied. The same beam-splitter-like picture reappears in CV memory models, where optical quadratures are mapped to spin-wave quadratures with finite write and read efficiencies (Cao et al., 2020, Yan et al., 2017).

In coherent transport models, TQE is usually cast as XX- or XY-type exchange. For Perfect State Transfer (PST) on an $N$-qubit chain,

$$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$

with

$$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$

In homogeneous quantum wires, the relevant control parameter is instead the endpoint coupling, tuned to an optimal value that scales as $N^{-1/6}$, so that the injected excitation forms an almost-linear wavepacket in $k$-space and arrives with little dispersion (Roy et al., 2024, Banchi et al., 2010, Banchi et al., 2011).

A third formal family is dispersive superexchange. In the minimal-resource register-transfer protocol, projecting a two-level coupler onto $|g\rangle$ yields

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$0

so that all pairs $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$1 can be transferred or swapped simultaneously in one step. Waveguide-QED and plasmonic models instead use master equations with collective dissipators and Green-function-mediated couplings, while giant-atom protocols enforce transfer through a dark-state constraint $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$2 under engineered chirality (Yang et al., 2014, Li et al., 2018, Wang et al., 7 Jun 2026).

3. Reversible light–matter transfer and quantum memories

In “Efficient reversible entanglement transfer between light and quantum memories” the entangled resource is a heralded single photon split into two paths and stored simultaneously in two spatially separated memories inside one cold-cesium MOT. The atomic levels are the $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$3 line of Cs, $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$4, $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$5, and $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$6, with optical depth up to $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$7. The DLCZ protocol is implemented in a small-OD slice, detection of Field-1 on APD1 heralds a collective excitation, readout yields a single photon with heralding efficiency $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$8, and the photon is delayed $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$9 in fiber before entering the EIT stage. The control beam is adiabatically switched off over $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$0, the photon is stored for $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$1, and Fabry–Perot cavities block control leakage by $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$2. The measured storage–retrieval efficiency peaks at $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$3 for $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$4; the reported operating value is $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$5. Nonclassicality is preserved, with $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$6, $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$7, $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$8, $$\hat\Psi(z,t)=\cos\theta(t)\,\hat E(z,t)-\sin\theta(t)\,\sqrt{N}\,\hat\sigma_{gs}(z,t)$$9, $\Omega(t)$0, $\Omega(t)$1, and entanglement transfer $\Omega(t)$2. The main decoherence channel is motional dephasing from beam angle, with lifetime $\Omega(t)$3 (Cao et al., 2020).

A deterministic multipartite variant is realized in “Establishing and storing of deterministic quantum entanglement among three distant atomic ensembles”. Three DOPAs generate one phase-squeezed and two amplitude-squeezed vacuum modes at $\Omega(t)$4, with identical squeezing parameter $\Omega(t)$5. After interference on $\Omega(t)$6 and $\Omega(t)$7, the three output modes form a CV GHZ-like entangled state, are chopped into $\Omega(t)$8 pulses, and are mapped by EIT into three $\Omega(t)$9Rb vapor cells. The write and read relations are

$N$0

with analogous expressions for $N$1. In the reported implementation, $N$2, $N$3, total round-trip efficiency $N$4, and the combined inseparability parameter is $N$5, confirming tripartite entanglement after storage and retrieval (Yan et al., 2017).

These memory experiments fix a central point in the TQE literature: transfer quality is not determined by fidelity alone, but by the joint preservation of efficiency, antibunching or quadrature squeezing, and a directly entanglement-sensitive witness.

4. Photonic interconversion, complex channels, and counterfactual transfer

A two-way photonic interface is demonstrated in “A two-way photonic quantum entanglement transfer interface”. The initial time–energy state is generated by cw-pumped SPDC and postselected on early and late time bins. Transfer to OAM is implemented by interferometric cyclic gates obeying

$N$6

while the reverse map is

$N$7

Experimentally the interface uses two fiber-based $N$8 unbalanced Franson interferometers, spiral-phase plates, a Dove-prism–Sagnac OAM sorter, and InGaAs SPDs gated at $N$9. The pre-transfer Franson visibility is $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$0. After $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$1 transfer, the four Bell-type OAM states attain average fidelity $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$2, purity $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$3, and two-photon OAM fringe visibility $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$4. After $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$5 transfer, the Franson visibility is $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$6. The overall entanglement-conversion success probability is $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$7 for $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$8 and effectively deterministic for $$H = \sum_{i=1}^{N-1} J_i (\sigma_i^+ \sigma_{i+1}^- + \sigma_i^- \sigma_{i+1}^+),$$9 (Huang et al., 2021).

Transport through a complex medium is treated differently in “Unscrambling Entanglement through a Complex Medium”. There the entangled state is encoded in a seven-dimensional Pixel basis, one photon traverses a $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$0 graded-index multimode fibre supporting $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$1 guided modes, and the fibre transmission matrix $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$2 is inferred from the entangled state itself. The key identity is

$$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$3

so inversion of the channel on Bob can be implemented by applying $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$4 on Alice. Before the fibre, correlations certify $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$5 to the $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$6-dimensional maximally entangled $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$7. After the fibre, without unscrambling, $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$8. After measuring $$J_i = J_0 \sqrt{i(N-i)}, \qquad t_{\rm PST}=\frac{\pi}{2J_0}.$$9 and applying $N^{-1/6}$0 on Alice’s SLM, the recovered state reaches $N^{-1/6}$1, exceeding the Schmidt-number-5 bound $N^{-1/6}$2 and certifying at least six-dimensional entanglement (Valencia et al., 2019).

A conceptually distinct limit is “Counterfactual quantum-information transfer”. In that protocol a nested Michelson interferometer, switchable polarization rotators, and a QD–cavity spin–photon interface generate a nonlocal entangled state without any photon or matter carrier traversing the channel. For large $N^{-1/6}$3, the outer- and inner-loop recursions yield

$N^{-1/6}$4

After a local Hadamard on Bob’s spin and a spin-basis measurement, one classical bit is communicated and Alice applies a conditional $N^{-1/6}$5 if needed. The protocol is explicitly contrasted with standard teleportation: no pre-shared entanglement resource is needed, and if a particle were to traverse the channel it would be detected and the protocol would fail (Guo et al., 2014).

5. Spin-pair, spin-chain, and superconducting-chain transfer

The elementary spin-exchange setting appears in “Quantum Entanglement transfer between spin-pairs”. Two target qubits interact with two source particles through Heisenberg couplings $N^{-1/6}$6 and $N^{-1/6}$7. When the source particles are two qubits and remain maximally entangled, the target-particle concurrence at $N^{-1/6}$8 reaches $N^{-1/6}$9, independent of the initial state of the targets. When the source particles are two qutrits, the maximum target entanglement after a single interaction depends on the initial target state and almost never reaches $k$0; however, repeated interaction with freshly prepared qutrit source pairs drives the target negativity monotonically toward $k$1 (Meng et al., 2010).

Long-distance coherent transfer through homogeneous wires is developed in “Optimal dynamics for quantum-state and entanglement transfer through homogeneous quantum wires”. For the XX case with $k$2, the optimal endpoint coupling is $k$3, with $k$4 and $k$5. For the XY chain with $k$6 and $k$7, the fitted scaling is $k$8, while $k$9 and $|g\rangle$0 for $|g\rangle$1. The central claim is that high-quality transfer does not require ad hoc engineering of the intrawire interactions nor a specific initial pulse shaping (Banchi et al., 2010).

The ballistic regime of an unmodulated XX spin bus sharpens this picture. In “Long quantum channels for high-quality entanglement transfer”, the endpoint coupling obeys

$|g\rangle$2

and the optimal large-$|g\rangle$3 peak amplitude tends to $|g\rangle$4. Consequently,

$|g\rangle$5

for arbitrarily long channels, and the transfer is almost independent of the channel initialization (Banchi et al., 2011).

A recent superconducting implementation is reported in “Parity-dependent state transfer for direct entanglement generation”. On a chain of six fixed-frequency transmon qubits with tunable couplers, the engineered PST couplings $|g\rangle$6 are realized with $|g\rangle$7. A single excitation placed on $|g\rangle$8 is transferred to $|g\rangle$9 at $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$00, with final population on $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$01 $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$02. In the multi-excitation regime the protocol produces a parity-dependent phase shift of $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$03 or $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$04, depending on the parity of the intermediate qubits, with $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$05 uncertainty. The same parity-dependent nonlocal interaction is then used to prepare a three-qubit GHZ state in one transfer operation, with raw overlap $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$06 and $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$07 after a single $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$08-phase correction on $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$09 (Roy et al., 2024).

6. Cavity, plasmonic, and giant-atom architectures

Multipartite TQE among cavities is addressed in “Transferring multipartite entanglement among different cavities”. A single coupler qubit $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$10 connects $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$11 cavities, and under large-detuning conditions the effective interaction becomes

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$12

Starting from an $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$13-qubit $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$14-class state in one register and vacuum cavities, evolution for

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$15

transfers the $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$16-state to the second register in a single step. Because no photon is excited in each cavity, photon-decay decoherence is suppressed; only one coupler qubit is needed and no classical pulses are used. For $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$17 in circuit QED with transmon qutrits, the optimized fidelity exceeds $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$18 for $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$19 (Su et al., 2016).

The minimal-resource generalization is “Single-step transfer or exchange of multipartite quantum entanglement with minimum resources”. There, a single two-level coupler $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$20 mediates arbitrary $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$21-qubit state transfer or exchange between two registers $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$22 and $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$23. Under dispersive conditions and the multiplexing constraint $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$24, the effective Hamiltonian

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$25

implements the simultaneous pairwise swap at

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$26

The gate time is independent of $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$27. Numerical master-equation simulations with realistic circuit-QED parameters yield transfer fidelities $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$28 and swap fidelities $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$29 (Yang et al., 2014).

At the nanophotonic scale, “Resonance Energy Transfer and Quantum Entanglement Mediated by Epsilon-Near-Zero and Other Plasmonic Waveguide Systems” analyzes two-level emitters coupled through lossy waveguides. The dissipative and coherent couplings are set by the dyadic Green function, and for an initially singly excited two-qubit state the concurrence is

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$30

In the ENZ waveguide, $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$31 for all separations up to a micron or more and $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$32, so $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$33 grows quickly to $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$34 and decays on the timescale $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$35, essentially independent of distance. Under coherent antisymmetric pumping, the steady-state concurrence reaches up to $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$36, and embedding a gain medium extends the concurrence lifetime by an order of magnitude. Detection is proposed through strong antibunching in $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$37 (Li et al., 2018).

A closely related but more recent direction is “Chiral Quantum Entanglement Transfer with Giant Atoms”. Giant atoms coupled at two points to a one-dimensional lattice support chiral spontaneous emission controlled by the phase $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$38. For pure right-chiral emission the system evolves into a dark subspace defined by

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$39

In the two-atom case, time-reversed Gaussian-like pulses implement a STIRAP-like transfer $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$40, while at mid-time the state becomes $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$41. Numerical scans give $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$42 and $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$43. Periodic piecewise modulation of the additional phase alternates chirality and yields stable, nearly lossless state exchange and steady entanglement even under non-Markovian conditions (Wang et al., 7 Jun 2026).

7. Figures of merit, trade-offs, and network significance

The TQE literature uses a heterogeneous set of figures of merit. In single-photon protocols these include storage–retrieval efficiency $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$44, cross-correlation $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$45, antibunching parameters such as $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$46 and $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$47, visibility $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$48, concurrence $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$49, and fidelity bounds such as $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$50. In CV settings the relevant witnesses are negativity $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$51 and the van Loock–Furusawa inequalities $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$52. In channel-unscrambling and high-dimensional work, Schmidt-number bounds and reconstructed-state fidelities are decisive. This suggests that TQE is a multi-objective task: efficiency, nonclassicality, dimensionality, brightness, and transport rate need not improve together.

That non-equivalence is explicit in motion-modulated excitation transfer. In “Motion-enhanced quantum entanglement in the dynamics of excitation transfer”, a chain of interacting molecules with oscillating inter-site distances develops a time-dependent coupling

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$53

For the two-site-plus-sink model, the average concurrence $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$54 is enhanced in a resonant window roughly $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$55, but the average sink population $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$56 decreases exactly in the same window. The enhancement persists for $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$57 and grows with the oscillation amplitude $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$58 until the perturbative description becomes questionable (Song et al., 2014).

Open-system cavity QED exhibits a different trade-off. In “Transferring entanglement to the steady-state of flying qubits”, two flying atoms interact with two cavities driven by non-Gaussian fields. In the good-cavity regime, a single-photon NOON state gives maximal transferred negativity

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$59

so for $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$60 one obtains $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$61. For entangled coherent states, the optimum $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$62 yields only $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$63, because the incommensurate Rabi frequencies of the Fock components cause destructive interference. In the bad-cavity limit, adiabatic elimination leads to a dissipation-dominated dynamics and very weakly quantum-correlated atomic systems, as witnessed by vanishing quantum discord (Guo et al., 2012).

A heralded DV-to-CV trade-off is quantified in “Transfer of entanglement from nonlocal photon to non-Gaussian CV states”. Two SMSV states are mixed with the two arms of a nonlocal single photon on identical beam splitters, and photon-number-resolving outcomes with $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$64 produce a maximally entangled parity-Bell state. The perfect-transfer probability

$$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$65

is optimized at $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$66 and $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$67, for which $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$68. If the SMSV inputs are first photon-subtracted, then for $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$69 the heralded probability becomes $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$70 for any $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$71. The cost is reduced brightness, because the effective squeezing $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$72 becomes small as $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$73 grows (Podoshvedov et al., 22 Sep 2025).

At the network level, the principal significance of TQE is rate scaling under repeated entanglement-distribution steps. For a $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$74 repeater chain, raising $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$75 from $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$76 to $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$77 reduces the entanglement distribution time by $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$78. In that context, the achieved $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$79 together with $$H = \int dz\,[\,g\,\hat E(z)\,\hat\sigma_{eg}(z) + \Omega(t)\,\hat\sigma_{es}(z) + h.c.\,].$$80 in reversible light–matter transfer is identified as a key enabler for multi-step entanglement swapping. The same literature points to longer-lived memories, multiplexing in temporal, spatial, OAM, or angular-frequency modes, active stabilization for remote nodes, and compact hybrid nodes that combine photonic interfaces with solid-state or atomic memories (Cao et al., 2020).