Classical and Quantum Resources in Perfect Teleportation

TL;DR

This paper addresses perfect teleportation of a qubit using partially entangled two-qutrit channels, investigating the trade-offs among the quantum channel, Alice's joint measurement, and Bob's classical information. By extending the standard two-qubit protocol and parameterizing Alice's measurement with an explicit unitary construction (including a five-parameter design) and subspace decompositions, the authors derive conditions for perfect teleportation and show a fundamental bound on the sum of entanglement and classical-communication resources. They demonstrate that their scheme achieves greater resource efficiency than prior protocols across the relevant channel class and establish a necessary and sufficient condition (max Schmidt coefficient ≤ 1/√2) for perfect teleportation in this framework, while revealing non-uniqueness and scalability limitations in higher dimensions. The findings illuminate a core resource-trade-off in quantum teleportation and point to open questions about scalable, low-dimensional extensions that preserve universality for perfect teleportation-enabled channels.

Abstract

We propose a teleportation protocol that enables perfect transmission of a qubit using a partially entangled two-qutrit quantum channel. Within our scheme, we analyze the relationship among the three key ingredients of teleportation: (i) the quantum channel, (ii) the sender's (Alice's) measurement operations, and (iii) the classical information transmitted to the receiver (Bob). Compared to Gour's protocol \cite{PRA2004}, our scheme requires less entanglement of Alice's measurement and fewer classical bits sent to Bob.Our results also show a trade-off between these two resources and derive a lower bound for their sum, quantifying their interplay in the teleportation process.

Figures (4)

• Figure 1: The quantum circuit diagram shows that qubit teleportation is realized with Alice's (top two wires) and Bob's (bottom wire) subsystems. The single lines denote qubits, and the double lines denote classical bits.
• Figure 2: Entanglement degree regimes for Alice's joint measurement and the quantum channel. (a) Results from Ref. PRA2004 scheme: red curve (case I) and magenta curve (case II). (b) Our proposed scheme (Section \ref{['ourscheme']}): red region (case I) and magenta region (case II). In addition, more specific parameter configurations are shown in (b). The blue curve shows case I with $\theta_2 = \pi/4$, $\theta_3 \in [0,\pi/4]$ and $\theta_1 =\frac{1}{2} \arctan(-\sqrt{2}\cot2\theta_3)$. The green curve shows case II with $\theta_1 = \pi/4$, $\theta_2 = 0$ and $\theta_3 \in [\arcsin\sqrt{1/3}, \pi/4]$.
• Figure 3: The classical bits sent to Bob vs. the entanglement of the quantum channel. The regions and curves of different colors correspond one-to-one with the various cases in Fig. 1b.
• Figure 4: The relationship between the total resources that Alice costs and the parameter $\theta_1$ when $a_0 = 0$.