[Paper Review] Noise-Resistant Quantum Teleportation, Ansibles, and the No-Projector Theorem

Samuel R. Hedemann|arXiv (Cornell University)|May 25, 2016

Quantum Information and Cryptography1 references3 citations

TL;DR

This paper proposes noise-resistant quantum teleportation (NRQT) using unassisted quantum error correction (UQEC) to protect quantum states from any noise without entanglement or ancilla qubits. By combining UQEC with teleportation, the method enables light-speed communication under physical connections, and suggests a 'no-projector theorem' analogous to the no-cloning theorem, implying superluminal communication (via an 'ansible') is impossible unless true projectors exist—though a pseudo-ansible for connection-free light-speed communication is realizable.

ABSTRACT

A method is presented for achieving entanglement-free teleportation of a quantum state subject to any quantum noise. We apply this as a light-speed noise-resistant communicator, but also treat the possibility of a quantum ansible, a device for effectively superluminal communication and quantum broadcasting. The results suggest a "no-projector theorem" analogous to the no-cloning theorem. We then show how to build a pseudo-ansible for connection-free light-speed communication.

Motivation & Objective

• To develop a method for teleporting quantum states unaffected by arbitrary quantum noise without requiring entanglement or ancilla qubits.
• To explore the theoretical possibility of superluminal communication via quantum projectors, leading to the concept of an 'ansible'.
• To establish a 'no-projector theorem' analogous to the no-cloning theorem, constraining the feasibility of true superluminal communication.
• To demonstrate that a connection-free, light-speed pseudo-ansible is achievable using UQEC and teleportation.

Proposed method

• Uses unassisted quantum error correction (UQEC) to protect quantum states from any noise channel without ancilla qubits or entanglement.
• Applies encoding and recovery operations using rank-1 projectors and reference states to correct errors via a sum over Kraus operators.
• Employs synchronized encoding/decoding operations $ L_j $ and $ L_j^ackslash dagger $, along with a recovery channel $ \mathcal{R} $, to reconstruct the original state after noise.
• Derives a universal recovery formula where the final state is proportional to $ \rho_D = \frac{1}{3}(I + \rho) $, allowing state extraction via $ \rho = 3\rho_D - I $.
• Demonstrates that the method works for any input state family with fixed eigenstates and variable eigenvalues, using only a single reference state.
• Shows that if true projectors exist, a superluminal 'ansible' could be built, but such projectors are ruled out by the proposed 'no-projector theorem'.

Experimental results

Research questions

• RQ1 Can quantum teleportation be made robust against arbitrary quantum noise without entanglement or ancilla qubits?
• RQ2 What are the implications of true quantum projectors for superluminal communication and the foundations of relativity?
• RQ3 Is there a fundamental principle analogous to the no-cloning theorem that forbids the existence of projectors enabling superluminal signaling?
• RQ4 Can a connection-free, light-speed communication device (a 'pseudo-ansible') be constructed using UQEC and teleportation?
• RQ5 How does unassisted quantum error correction enable universal protection of quantum states under any noise channel?

Key findings

• The method achieves noise-resistant quantum teleportation (NRQT) by combining UQEC with teleportation, enabling reliable state transfer under any noise channel.
• The recovery process yields a final state $ \rho_D = \frac{1}{3}(I + \rho) $, from which the original state $ \rho $ can be reconstructed via $ \rho = 3\rho_D - I $, ensuring fidelity regardless of noise.
• The derivation shows that the error-dependent scalar $ C = \sum_{q,k} |(E_k)_{q,1}|^2 $ equals 1 for all channels, validating the universality of the correction.
• A 'no-projector theorem' is proposed, implying that superluminal communication via an 'ansible' is impossible unless true projectors exist.
• A pseudo-ansible for connection-free, light-speed communication is theoretically realizable using only UQEC and teleportation, without requiring physical links.
• The method works universally for any input state family with fixed eigenstates and variable eigenvalues, using only a single reference state and no ancilla.