Quantum teleportation of an unknown quantum state necessitates the transmission of two classical bits of information; however, when the quantum state is partially known, only a single classical bit is required for the teleportation of its quantum coherence. In this study, we explore the teleportation of quantum coherence through noisy channels utilizing merely one classical bit of information. Our findings reveal that, in contrast to noise-free scenarios, the generalized Bell states POVM (GBS-POVM) and non-maximally entangled states may surpass the performance of Bell states POVM (BS-POVM) and maximally entangled states in enabling probabilistic teleportation of quantum coherence. Nevertheless, when assessing the average amount of quantum coherence that can be teleported, maximally entangled states combined with BS-POVM emerges as the optimal choice, regardless of the type of noise encountered. Moreover, we uncover that for bit-phase-flip (BPF) noise, it is feasible to construct a suitable GBS-POVM that completely mitigates this noise. For other types of noise, we demonstrate that enhancing the teleportation of quantum coherence can be accomplished through entangling two consecutive uses of the same noisy channel, i.e., correlated noise. Notably, correlation effects arising from Pauli channels can entirely negate the detrimental impact of Pauli noises on the teleportation process for quantum coherence.
Quantum teleportation of an unknown quantum state necessitates the transmission of two classical bits of information; however, when the quantum state is partially known, only a single classical bit is required for the teleportation of its quantum coherence. In this study, we explore the teleportation of quantum coherence through noisy channels utilizing merely one classical bit of information. Our findings reveal that, in contrast to noise-free scenarios, the generalized Bell states POVM (GBS-POVM) and non-maximally entangled states may surpass the performance of Bell states POVM (BS-POVM) and maximally entangled states in enabling probabilistic teleportation of quantum coherence. Nevertheless, when assessing the average amount of quantum coherence that can be teleported, maximally entangled states combined with BS-POVM emerges as the optimal choice, regardless of the type of noise encountered. Moreover, we uncover that for bit-phase-flip (BPF) noise, it is feasible to construct a suitable GBS-POVM that completely mitigates this noise. For other types of noise, we demonstrate that enhancing the teleportation of quantum coherence can be accomplished through entangling two consecutive uses of the same noisy channel, i.e., correlated noise. Notably, correlation effects arising from Pauli channels can entirely negate the detrimental impact of Pauli noises on the teleportation process for quantum coherence.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a lesser number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a non-maximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's lab in terms of the composition of the completely positive maps corresponding to the shared resource state and joint POVM performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is possible perfectly with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with the Werner states and show that even when the Werner states become separable, the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement.
Abstract In this paper quantum teleportation of an unknown quantum state via noisy maximally bipartite (Bell) and maximally tripartite (Greenberger–Horne–Zeilinger (GHZ)) entangled states are investigated. We suppose that one of the observers who would receive the sent state accelerates uniformly with respect to the sender. The interactions of the quantum system with its environment during the teleportation process impose noises. These (unital and nonunital) noises are: phase damping, phase flip, amplitude damping and bit flip. In expressing the modes of the Dirac field used as qubits, in the accelerating frame, the so-called single mode approximation is not imposed. We calculate the fidelities of teleportation, and discuss their behaviors using suitable plots. The effects of noise, acceleration and going beyond the single mode approximation are discussed. Although the Bell states bring higher fidelities than GHZ states, the global behaviors of the two quantum systems with respect to some noise types, and therefore their fidelities, are different.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a smaller number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a nonmaximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's laboratory in terms of the composition of the completely positive maps corresponding to the shared resource state and a joint positive operator-valued measure (POVM) performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is perfectly possible with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with Werner states and show that even when Werner states become separable, the amount of teleported coherence is nonzero, implying the possibility of teleportation of coherence without entanglement.
Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.
In the domain of quantum communication, quantum teleportation (QT) emerges as a pivotal protocol, enabling the transmission of quantum states across significant distances. However, the ubiquitous presence of quantum noise inevitably affects this process, causing deviations in the teleported state from its intended configuration. This study proposes an innovative approach to mitigate noise error (bit-flip and phase-flip) and within quantum channels. The method involves implementing quantum gates between communicating parties, effectively diminishing the impact of these noise types on the entangled channel and enhancing QT efficacy in noise-prone environments. Experimental results demonstrate that noisy channel has low-fidelity 16.67% in bit flip noise and 68.60% in phase flip noise. The proposed noise mitigation quantum circuit attained the 100% fidelity.
Abstract The purpose of this paper is to further investigate the correlated and memory effects in 3D-Pauli-like noisy channels for controlled teleportation of an arbitrary unknown single-qutrit state. We first construct a three-qutrit maximally entangled state in a three-dimensional (3D) Hilbert space and subsequently propose a 3D controlled quantum teleportation (CQT) scheme for an arbitrary unknown single-qutrit state using the constructed three-qutrit maximally entangled state as the quantum channel. In this ideal case, through a few simple 3D unitary operations, the two communicating parties can perfectly accomplish the teleportation task under the supervision of the controller. Subsequently, we examine the performance of this CQT scheme under two successive uses of a 3D-Pauli-like noisy channel with memory, where the noise errors are categorized into four types: trit-flip, t-phase-flip, trit-phase-flip, and t-depolarizing. For each noise type, an analytical expression of the average fidelity is derived as a function of both the noise and memory parameters. Specifically, we find that, regardless of the noise strength, memory enhances the average fidelity for trit-flip and t-depolarizing noises, whereas for t-phase-flip and trit-phase-flip noises, memory reduces the average fidelity once the noise intensity exceeds a certain threshold. This indicates that in the first two noisy channels, memory can improve the communication efficiency of CQT, while in the latter two, excessive noise causes memory to diminish the teleportation performance.