Quantum Teleportation is a two-party functionality that enables the transfer of an arbitrary unknown quantum state from one party (Alice) to another (Bob), without physically transmitting the particle carrying the state [1]. This quantum task is accomplished using two key resources:

• A pre-shared entangled pair between Alice and Bob.
• Two bits of classical communication from Alice to Bob.

In more formal cryptographic terms, quantum teleportation realises a non-local quantum state transfer functionality, where the output state on Bob’s side is (up to local correction) identical to Alice’s original input state, even though that state was never directly sent. The quantum information is destroyed on Alice’s side during the process, ensuring no-cloning is respected.

This functionality is foundational in quantum communication and quantum cryptographic protocols, and underpins quantum network routing, quantum repeaters, and many delegated quantum computation schemes.

This functionality is quantum in nature and has no classical counterpart.

This functionality is used in many other higher-level quantum functionalities over a quantum network, such as delegated quantum computations or tests of quantumness. 

One of the important applications of quantum teleportation is in quantum repeaters, which are crucial for large-scale quantum networks.

Deterministic and perfect: Quantum teleportation succeeds deterministically, assuming ideal entanglement and perfect measurement, and introduces no information loss.

Natural Privacy:
The original functionality has no cryptographic requirement as such; however, if the entanglement is private and secure, the teleportation preserves the confidentiality of the quantum state. Eavesdropping is prevented unless the entangled resource or classical channel is compromised.

Resources: Requires one entangled qubit pair and two bits of classical communication to teleport one qubit.

Teleportation-Based Computation: Models such as MBQC rely on teleportation steps (gate teleportation) to implement universal quantum computation via measurements and corrections [2].

1. Bennett, Charles H., Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.” Physical review letters 70, no. 13 (1993): 1895.
2. Briegel, Hans J., David E. Browne, Wolfgang Dür, Robert Raussendorf, and Maarten Van den Nest. “Measurement-based quantum computation.” Nature Physics 5, no. 1 (2009): 19-26.