[Paper Review] A single quantum cannot be teleported

Daniele Tommasini|ArXiv.org|Oct 9, 2002

Quantum Information and Cryptography10 references3 citations

TL;DR

This paper argues that perfect quantum teleportation of a single qubit is fundamentally impossible due to quantum field theory's inherent uncertainty in particle number, even when the original state is destroyed. The author demonstrates that teleportation cannot achieve infallible state transfer, introducing an unavoidable theoretical error at the percent level or smaller, thus generalizing the no-cloning theorem to include destructive copying protocols.

ABSTRACT

Due to the Heisemberg uncertainty principle, it is impossible to design a procedure which permits perfect cloning of an arbitrary, unknown "qubit" (the spin or polarization state of a single quantum system)1,2. However, it is believed that a perfect copying protocol can be achieved, at least in principle, if the qubit to be copied is destroyed in the original system. Quantum teleportation3,4 is supposed to allow for such a result. Here, this belief is shown to be invalidated by a fundamental uncertainty about the number of particles involved in any process, as predicted by Quantum Field Theory. As a result, teleportation cannot provide an infallible copying procedure for the single qubits, not even in the limit of perfect experimental sensitivities. The no-cloning theorem1,2 can then be generalized to the case of destroying the original. Teleportation remains an interesting statistical procedure, having an unavoidable theoretical error at the percent level or few orders of magnitude smaller, depending on the physical process that is used. Although it cannot be made arbitrarily small, such an error is small enough to remain hidden in present experiments.

Motivation & Objective

• To investigate whether quantum teleportation can serve as a perfect copying procedure for single qubits, even when the original state is destroyed.
• To examine the role of particle number uncertainty in quantum field theory as a fundamental obstacle to perfect teleportation.
• To challenge the widely held belief that teleportation enables infallible state transfer by identifying an unavoidable theoretical error.
• To generalize the no-cloning theorem to include protocols that destroy the original state, extending its scope beyond standard cloning.
• To assess the practical implications of this theoretical error in current and future experimental quantum technologies.

Proposed method

• The paper applies principles from quantum field theory to analyze the fundamental uncertainty in the number of particles involved in any quantum process.
• It examines the implications of this uncertainty for quantum teleportation protocols, particularly in the context of single-qubit states.
• The analysis focuses on the impossibility of precisely determining whether a single quantum system is being teleported or multiple systems are involved.
• The author uses theoretical reasoning to show that the uncertainty in particle number introduces a fundamental error in teleportation, regardless of experimental precision.
• The argument is based on the non-conservation of particle number in relativistic quantum field theory, which undermines the assumption of a single source qubit.
• The paper derives that the error in teleportation cannot be made arbitrarily small, setting a theoretical lower bound at the percent level or smaller.

Experimental results

Research questions

• RQ1 Can quantum teleportation achieve perfect state transfer of a single qubit, even when the original state is destroyed?
• RQ2 What is the role of particle number uncertainty in quantum field theory in limiting the fidelity of quantum teleportation?
• RQ3 Is there a fundamental theoretical error in teleportation that prevents it from being an infallible copying procedure?
• RQ4 Can the no-cloning theorem be extended to include protocols that destroy the original state?
• RQ5 How does the unavoidable error in teleportation compare to experimental sensitivities in current quantum technologies?

Key findings

• Perfect teleportation of a single qubit is fundamentally impossible due to quantum field theory's inherent uncertainty in particle number.
• The theoretical error in teleportation is unavoidable and cannot be reduced below the percent level or smaller, depending on the physical process.
• This error invalidates the belief that teleportation can serve as a perfect copying procedure, even when the original state is destroyed.
• The no-cloning theorem is generalized to include destructive copying protocols, showing that no such protocol can achieve perfect fidelity.
• The error is small enough to remain hidden in current experiments, but it remains a fundamental limitation in principle.