Experimental Test of Quantum No-Hiding Theorem

TL;DR

This paper reports an experimental verification of the quantum no-hiding theorem using nuclear magnetic resonance, demonstrating that information lost in a bleaching process can be recovered in ancillary qubits, thus supporting fundamental quantum principles.

Contribution

The first experimental test of the quantum no-hiding theorem using NMR techniques, confirming theoretical predictions about information recovery after bleaching.

Findings

Information can be fully recovered from ancilla qubits.

NMR effectively tests fundamental quantum theorems.

Supports the robustness of quantum information.

Abstract

Linearity and unitarity are two fundamental tenets of quantum theory. Any consequence that follows from these must be respected in the quantum world. The no-cloning theorem and the no-deleting theorem are the consequences of the linearity and the unitarity. Together with the stronger no-cloning theorem they provide permanence to quantum information, thus, suggesting that in the quantum world information can neither be created nor be destroyed. In this sense quantum information is robust, but at the same time it is also fragile because any interaction with the environment may lead to loss of information. Recently, another fundamental theorem was proved, namely, the no-hiding theorem that addresses precisely the issue of information loss. It says that if any physical process leads to bleaching of quantum information from the original system, then it must reside in the rest of the universe with no information being hidden in the correlation between these two subsystems. This has applications in quantum teleportation, state randomization, private quantum channels, thermalization and black hole evaporation. Here, we report experimental test of the no-hiding theorem with the technique of nuclear magnetic resonance (NMR). We use the quantum state randomization of a qubit as one example of the bleaching process and show that the missing information can be fully recovered up to local unitary transformations in the ancilla qubits. Since NMR offers a way to test fundamental predictions of quantum theory using coherent control of quantum mechanical nuclear spin states, our experiment is a step forward in this direction.