We investigate the standard quantum teleportation protocol for a single-qubit state, focusing on the scenario where the qubit undergoes a class of non-unitary evolution governed by parity-time ( \mathcal{PT} 𝒫 𝒯 )-symmetric non-Hermitian Hamiltonians. Additionally, we examine the case where the entangled pair shared by Alice and Bob is exposed to a noise channel. In the \mathcal{PT} 𝒫 𝒯 -symmetric regime, the teleportation fidelity exhibits time-dependent oscillations. Compared to the conventional case without non-Hermitian operations, periodic enhancements in fidelity are observed, and we analytically derive their dependence on the parameters of both the non-Hermitian Hamiltonian and noise channel. When the \mathcal{PT} 𝒫 𝒯 symmetry is broken, the fidelity ceases to oscillate and instead decays to a steady value. Notably, even in this regime, non-Hermitian operations can yield fidelity improvements over conventional schemes. We further investigate the teleportation of quantum Fisher information (QFI) and find that its evolutionary behavior differs from that of fidelity. Analytical results reveal that QFIs corresponding to different estimated parameters exhibit distinct outcomes at Bob’s receiving end during teleportation. Furthermore, we derive a trade-off inequality between fidelity and QFI, offering a theoretical tool to coordinately optimize these two quantities in the teleportation process.
We investigate the standard quantum teleportation protocol for a single-qubit state, focusing on the scenario where the qubit undergoes a class of non-unitary evolution governed by parity-time ( \mathcal{PT} 𝒫 𝒯 )-symmetric non-Hermitian Hamiltonians. Additionally, we examine the case where the entangled pair shared by Alice and Bob is exposed to a noise channel. In the \mathcal{PT} 𝒫 𝒯 -symmetric regime, the teleportation fidelity exhibits time-dependent oscillations. Compared to the conventional case without non-Hermitian operations, periodic enhancements in fidelity are observed, and we analytically derive their dependence on the parameters of both the non-Hermitian Hamiltonian and noise channel. When the \mathcal{PT} 𝒫 𝒯 symmetry is broken, the fidelity ceases to oscillate and instead decays to a steady value. Notably, even in this regime, non-Hermitian operations can yield fidelity improvements over conventional schemes. We further investigate the teleportation of quantum Fisher information (QFI) and find that its evolutionary behavior differs from that of fidelity. Analytical results reveal that QFIs corresponding to different estimated parameters exhibit distinct outcomes at Bob’s receiving end during teleportation. Furthermore, we derive a trade-off inequality between fidelity and QFI, offering a theoretical tool to coordinately optimize these two quantities in the teleportation process.
Abstract Quantum teleportation, a cornerstone of quantum information processing, faces critical challenges from environmental noise such as amplitude damping (AD), which degrades entanglement and reduces teleportation fidelity below the classical limit of 2/3. This study investigates the role of parity-time ( PT ) symmetric operations, a type of non-Hermitian operation, in enhancing teleportation fidelity under AD noise. We first derive the explicit dynamics of entangled states subjected to AD noise using Kraus operators, showing that the average fidelity decays monotonically with increasing decoherence strength. By introducing local PT symmetric operations, we show the average fidelity exhibits periodic linear oscillations, with minimum values increasing with non-Hermiticity and remaining above 2/3, while maximum fidelity consistently reaches the optimal value of 1. These results confirm that non-Hermitian operations effectively protect quantum teleportation fidelity, maintaining stability and optimal performance despite parameter variations. Experimental feasibility is discussed using nuclear magnetic resonance systems with duality quantum computing techniques.
Abstract We investigate the effect of local parity-time ( PT ) symmetric operation on quantum teleportation in non-Markovian environments, focusing on resonant and off-resonant regimes. An exactly solvable two-qubit model with independent structured reservoirs is built to derive the average teleportation fidelity. We show that the PT symmetric operation lead to oscillatory fidelity decay with local revivals instead of monotonic decay, and optimally PT symmetric operation can stably keep the average fidelity above the classical 2/3 limit even in off-resonant non-Markovian regimes, effectively protecting the quantum advantage of teleportation.
In this work, we consider the following teleportation protocol: There is an arbitrary two-qubit resource state, shared between two spatially separated parties, Alice and Bob. Applying local unitary operators, they transform the resource state into the canonical form. To teleport an unknown qubit, Alice now measures her qubits in the Bell basis. Then, the measurement outcome is communicated by Alice to Bob via noisy classical channel(s). Finally, after receiving the classical message, Bob applies the necessary unitary operator to his qubit. Under this protocol, we find the exact formulae of teleportation fidelity and its deviation. We further find conditions for non-classical fidelity within this protocol. If the classical communication is noiseless in the above protocol then there are resource states which can lead to zero fidelity deviation. However, we show that such states may not lead to zero fidelity deviation when the classical communication is noisy in the same protocol. We also explore the opposite case, i.e., the states, which cannot lead to zero fidelity deviation in the above protocol when the classical communication is noiseless, may lead to zero fidelity deviation when the classical communication is noisy in the same protocol without compromising the non-classical fidelity. Moreover, we exhibit scenarios within the present protocol, where the fidelity deviation increases if the entanglement of the resource state is increased.
Achieving near-unity fidelity of Quantum Teleportation (QT) in a noisy environment is an essential requirement for its real-world applications. Towards this goal, we devise a distinctive protocol based on the timing of the sender Alice's Bell-basis measurement, synchronous with the suitably engineered structure of noise in the receiver Bob's wing, without requiring any knowledge or manipulation of Alice's local noise. For this purpose, to finally obtain the teleported states by performing the required unitary operations, Bob has to retain his qubits for only two particular Bell-basis outcomes communicated by Alice, whose corresponding reduced states have no dependence on the noise parameters in Alice's wing. Such postselection is crucial for enhancing the fidelity of the teleported state towards its ideal limit, while ensuring its full independence of Alice's noise. We formulate the specifics of our protocol in terms of a generic two-level quantum system, subjected to a general non-Markovian spin-boson model for dephasing noise. The proposed scheme is illustrated by using any pure maximally/non-maximally entangled state as well as a Werner-type mixed state as resource. In particular, using resource states having small values of entanglement measure, we show that the high fidelity of QT is achievable in the presence of noise. Further, using our scheme, considering even the local regime of Werner states, wherein the Bell-CHSH inequalities are not violated, we show that the QT fidelity in the presence of noise can be appreciably high.
Abstract Quantum teleportation fidelity is severely degraded by environmental noise, especially correlated amplitude damping (CAD) decoherence with non-negligible memory effects, which is more practical in high-rate transmission. This paper investigates enhancing teleportation fidelity under CAD noise using parity-time ( PT ) symmetric operation, we first analyze teleportation dynamics under CAD, showing its average fidelity outperforms uncorrelated amplitude damping. Moreover, we show that the PT symmetric operation could drastically enhance the fidelity in CAD noise. Results demonstrate PT symmetric operation significantly boost average fidelity, which remains above the classical limit of 2/3. Optimized via adjusting non-Hermitian parameters, the fidelity can even reach 1. Our results extend the ability of PT symmetric operation as a technique in various quantum information processes which are affected by correlated noise.
Abstract Quantum Fisher Information (QFI), which sets the fundamental bound on parameter estimation precision via the quantum Cramér-Rao inequality, is investigated for a general single-mode Gaussian state before and after teleportation. Using a two-mode squeezed vacuum state as a shared entanglement resource between Alice and Bob, we analyze the teleportation protocol under environmental noise, focusing on diffusion and dissipation induced by a thermal bath. By comparing QFI for several parameters of the input state before and after teleportation, we evaluate the effectiveness of QFI transfer. We find that increasing the squeezing of the shared state enhances QFI preservation. Notably, under certain conditions, environmental interactions can help maintain QFI, particularly for shared states with high frequency, suggesting a subtle interplay between system dynamics and decoherence.