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arXiv:2608.11314

Teleportation through time-varying channels: threshold geometry and a complete-positivity bound on non-Markovian backflow

Chaibata Seida

quant-phSubmitted Aug 11, 2026• Announced Aug 13, 2026• 0 citations
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Abstract

A Bell pair distributed through a link that combines amplitude damping with dephasing at time-dependent rates has dynamics that separate into a fixed part and a moving one. The negativity, fully entangled fraction, discord, and average teleportation fidelity depend on time only through the accumulated damping parameters $p(t)$ and $q(t)$. Every threshold is therefore a curve fixed in the unit square, and the rates select nothing but a trajectory across it. The Horodecki fidelity formula $\bar{F} = \frac{1}{2} + \frac{1}{6}\mathrm{Tr}|T|$ covers one- and two-sided exposure alike: the condition $\det T \leq 0$ under which it takes this form holds throughout the unit square for both. Under symmetric two-sided noise the entanglement vanishes when $p+q\geq1$, where the exact relation $\bar{F}^{2s}=\frac{2}{3}+\frac{1}{3}\mathcal{N}_{2s}$ ties disentanglement and the loss of quantum advantage to the same instant. One-sided exposure admits no finite-time sudden death for any rate profile, and the discord stays strictly positive throughout the open square, so the distributed state can be separable, useless for teleportation, and still nonclassical. For harmonically modulated rates, complete positivity caps the backflow at one modulation period of static decay, $ΔΓ_{k}\leq2πγ_{k,0}/Ω$, equivalently at a modulation depth $ξ_{k}\leq4.6033$ independent of $Ω$. Inside that window the trajectory reverses, producing finite intervals of restored quantum advantage and entanglement sudden birth.

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A Bell pair distributed through a link that combines amplitude damping with dephasing at time-dependent rates has dynamics that separate into a fixed part and a moving one. The negativity, fully entangled fraction, discord, and average teleportation fidelity depend on time only through the accumulated damping parameters p(t)p(t)p(t) and q(t)q(t)q(t). Every threshold is therefore a curve fixed in the unit square, and the rates select nothing but a trajectory across it. The Horodecki fidelity formula Fˉ=12+16Tr∣T∣\bar{F} = \frac{1}{2} + \frac{1}{6}\mathrm{Tr}|T|Fˉ=21​+61​Tr∣T∣ covers one- and two-sided exposure alike: the condition det⁡T≤0\det T \leq 0detT≤0 under which it takes this form holds throughout the unit square for both. Under symmetric two-sided noise the entanglement vanishes when p+q≥1p+q\geq1p+q≥1, where the exact relation Fˉ2s=23+13N2s\bar{F}^{2s}=\frac{2}{3}+\frac{1}{3}\mathcal{N}_{2s}Fˉ2s=32​+31​N2s​ ties disentanglement and the loss of quantum advantage to the same instant. One-sided exposure admits no finite-time sudden death for any rate profile, and the discord stays strictly positive throughout the open square, so the distributed state can be separable, useless for teleportation, and still nonclassical. For harmonically modulated rates, complete positivity caps the backflow at one modulation period of static decay, ΔΓk≤2πγk,0/ΩΔΓ_{k}\leq2πγ_{k,0}/ΩΔΓk​≤2πγk,0​/Ω, equivalently at a modulation depth ξk≤4.6033ξ_{k}\leq4.6033ξk​≤4.6033 independent of ΩΩΩ. Inside that window the trajectory reverses, producing finite intervals of restored quantum advantage and entanglement sudden birth.
We study Bell-mixing lines ρλ=λΦ++(1−λ)σρ_λ=λΦ^+ +(1-λ)σρλ​=λΦ++(1−λ)σ, where Φ+Φ^+Φ+ is a fixed Bell reference and σσσ is a separable two-qubit noise state. Along this line there are two operational crossings: the state becomes entangled, and it reaches quantum teleportation advantage over classical strategies. We package these crossings as capacities of the noise state. The entanglement absorption capacity Cabs(σ)C_{\rm abs}(σ)Cabs​(σ) is the largest amount of Bell reference that σσσ can absorb while the partial transpose remains positive. The fidelity absorption capacity CF(σ)C_F(σ)CF​(σ) is the largest amount of Bell reference that σσσ can absorb while keeping the maximal teleportation fidelity at or below the classical bound 2/32/32/3. The thresholds corresponding to the two crossing points are obtained from the same Möbius map, λ∗=Cabs/(1+Cabs)λ_* = C_{\rm abs}/(1+C_{\rm abs})λ∗​=Cabs​/(1+Cabs​) and λF=CF/(1+CF)λ_F = C_F/(1+C_F)λF​=CF​/(1+CF​). We derive closed-form capacities and thresholds for product noise states and separable complex XXX noise states. For product noise, CabsC_{\rm abs}Cabs​ depends only on local marginal purities, while CFC_FCF​ also depends on orientation relative to the maximally entangled reference. For XXX noise states, both capacities are explicit in all four Bell frames. We also study three extensions: arbitrary pure-state references, the evolution of XXX noise states and their capacities under local amplitude-damping and dephasing channels, and decomposition certificates that give lower bounds on the capacities, hence on the thresholds, for general separable noise.
Abstract Quantum teleportation fundamentally depends on shared quantum correlations between spatially separated parties. Although entanglement is widely recognized as the primary resource enabling teleportation, quantum discord represents a more general form of nonclassical correlations that can persist even when entanglement is absent. We provide a thorough analysis combining analytical and numerical evaluations of quantum discord, negativity, and concurrence across varying noise parameters. The study includes simulations under both ide-alized and realistic noisy conditions, incorporating depolarizing noise models alongside experimentally relevant constraints. To improve quantum fidelity and accurately characterize quantum correlations in noisy environments, advanced error mitigation techniques—such as measurement error correction and zero-noise extrapolation—are applied. In this study, we focus on teleportation protocols utilizing two-qubit Werner states, which constitute a significant class of noisy mixed states modeling imperfect entanglement. We systematically examine how the teleportation fidelity varies as a function of the Werner mixing parameter λ and investigate its relationship with the corresponding quantum discord. Our findings indicate that quantum discord remains strictly greater than zero even in parameter regions where entanglement vanishes, emphasizing the role of discord in sustaining quantum advantages in teleportation schemes exposed to noise and imperfections. This highlights the importance of considering non-entanglement quantum correlations for a comprehensive understanding of teleportation resources in realistic settings.
This study compares the effects of Markovian and non-Markovian noise channels on a standard Bell state-based quantum teleportation protocol. Amplitude damping, phase damping, depolarising, and time-dependent (non-Markovian) channels were analysed within the same simulation framework, and teleportation fidelity was calculated as a function of noise intensity. Critical noise parameters were determined with reference to the classical threshold value (F=2/3), entanglement dynamics were evaluated using concurrence, and entanglement sudden death (ESD) points were identified. Non-Markovian behaviour was quantitatively analysed using the Breuer–Laine–Piilo (BLP) metric. The results show that different noise mechanisms significantly affect teleportation performance, and that entanglement conservation and operational teleportation advantages do not always coincide. Numerical results were validated by analytical comparison
We investigate the time evolution of negativity and quantum discord for a pair of non-interacting qubits with one being weakly coupled to a decohering Davies-type Markovian environment. At initial time of preparation, the qubits are prepared in one of the maximally entangled pure Bell states. In the limiting case of pure decoherence (i.e. pure dephasing), both the quantum discord and negativity decay to zero in the long time limit. In the presence of a manifest dissipative dynamics, the entanglement negativity undergoes a sudden death at finite time, while the quantum discord relaxes continuously to zero with increasing time. We find that in dephasing environments, the decay of the negativity is more propitious with increasing time; in contrast, the evolving decay of the quantum discord proceeds more weakly for dissipative environments. Particularly, the slowest decay of the quantum discord emerges when the energy relaxation time matches the dephasing time.
In distributed quantum computing, quantum networks provide a potential infrastructure for long-range quantum information processing. Controlled quantum teleportation (CQT) is a key practically relevant protocol that can connect two parties on a network and enables a third party, the controller to allow or abort the secure teleportation of an arbitrary single-qubit state between the two parties. We investigate the robustness of a three-qubit GHZ resource under bit-flip, phase-flip, depolarizing, and amplitude-damping noise. Using the Kraus-operator formalism, we characterize the noisy resource through multipartite quantum discord, genuine multipartite concurrence (GMC), localizable entanglement (LE), and CQT fidelity. We also outline a proof-of-concept photonic implementation for preparing the three-qubit GHZ resource and realizing the CQT protocol, which could enable experimental investigation of the effects of noise. Our results show that bit-flip and amplitude-damping noise generally preserve useful mutipartite quantum correlations over broader noise parameter ranges. Interestingly, multipartite discord exhibits freezing under bit-flip noise over a finite parameter regime. Moreover, discord can persist beyond the sudden death of genuine multipartite entanglement, revealing the distinct robustness of nonclassical correlations. We further demonstrate that CQT fidelity which characterizes the performance of CQT can exceed the classical threshold even after GMC vanishes, while LE more closely reflects the operational usefulness of the noisy resource. These findings highlight the complementary roles of quantum correlations and entanglement in assessing the resilience of GHZ-based protocols.
We investigate quantum teleportation through dissipative channels and calculate teleportation fidelity as a function of damping rates. It is found that the average fidelity of teleportation and the range of states to be teleported depend on the type and rate of the damping in the channel. Using the fully entangled fraction, we derive two bounds on the damping rates of the channels: one is to beat the classical limit and the second is to guarantee the nonexistence of any other copy with better fidelity. The effect of the initially distributed maximally entangled state on the process is presented; the concurrence and the fully entangled fraction of the shared states are discussed. We intend to show that prior information on the dissipative channel and the range of qubit states to be teleported is helpful for the evaluation of the success of teleportation, where success is defined as surpassing the fidelity limit imposed by the fidelity of the 1-to-2 optimal cloning machine for the specific range of qubits.