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Chinese Physics B

Uncertainties of the standard quantum teleportation channel

Zhihua 志华 Zhang 章, Zehao Guo, Zhipeng 志鹏 Qiu 邱

Published Feb 5, 2025• 1 citation
Publisher

Abstract

Abstract From the perspective of state-channel interaction, standard quantum teleportation can be viewed as a communication process characterized by both input and output, functioning as a quantum depolarizing channel. To achieve a precise quantification of the quantumness introduced by this channel, we examine its uncertainties, which encompass both state-dependent and state-independent uncertainties. Specifically, for qudit systems, we provide general formulas for these uncertainties. We analyze the uncertainties associated with standard quantum teleportation when induced by isotropic states, Werner states, and X-states, and we elucidate the correlation between these uncertainties and the parameters of the specific mixed states. Our findings demonstrate the validity of quantifying these uncertainties.

DOI
10.1088/1674-1056/adb263

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Teleportation for pure states, mixed states with standard and optimal protocols are introduced and investigated systematically. An explicit equation governing the teleportation of finite dimensional quantum pure states by a generally given non-local entangled state is presented. For the teleportation of a mixed state with an arbitrary mixed state resource, an explicit expression is obtained for the quantum channel associated with the standard teleportation protocol. The corresponding transmission fidelity is calculated. It is shown that the standard teleportation protocol is not optimal. The optimal quantum teleportation is further studied, its fidelity is given and shown to be related to the fully entangled fraction of the quantum resource, rather than the single fraction as in the standard teleportation protocol.
The conventional certification method for quantum teleportation protocols relies on surpassing the highest achievable classical average fidelity between target and teleported states. Our paper highlights the limitations of this approach: inconsistent conclusions can be obtained when considering different distance measures in the quantum state space, leading to contradictory interpretations. In particular, this behavior is manifested when modeling a very common noisy experimental scenario, in which the resource state takes the form of a Werner state generated by the influence of a depolarizing channel acting on the Bell state resource. Two additional noise models, based on amplitude-damping channels, are also analyzed. Our paper, therefore, stresses the necessity of new certification methods for quantum teleportation.
Quantum teleportation of an n-qubit state performed using as an entangled resource a general bipartite state of 2n qubits instead of n Bell states is equivalent to a correlated Pauli channel. This yields a new characterization of such channels in terms of many-body correlation functions of the teleporting media. It provides a relatively simple method for determining whether a correlated quantum channel is able to reliably convey quantum messages by studying the entanglement properties of the teleportation mediating system. Our model is then generalized to the continuous-variable case.
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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.