Quantum Cost Efficient Scheme for Violating the Holevo Bound and Cloning in the Presence of Deutschian Closed Timelike Curves

TL;DR

This paper presents a quantum scheme that efficiently stores, retrieves, and clones classical information in the presence of Deutschian closed timelike curves, violating the Holevo bound with linear quantum cost.

Contribution

It introduces a new quantum cost-efficient protocol for information storage, retrieval, and cloning using D-CTCs, outperforming previous exponential-cost schemes.

Findings

Quantum cost is of order O(n) for the proposed schemes.

The schemes successfully violate the Holevo bound.

They enable faithful cloning of qubits with reduced quantum resources.

Abstract

Brun \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 210402 (2009)] showed that in the presence of a Deutschian closed timelike curve (D-CTC), one could violate the Holevo bound. It is possible to utilize the Holevo bound violation to encode $n$-bit classical information in a single qubit. Here we demonstrate a new quantum cost efficient scheme, for storing and retrieving $n$-bit classical information faithfully in the presence of a D-CTC in violation of the Holevo bound. We also propose a new protocol for cloning a qubit in the presence of a D-CTC. In both the schemes, the quantum cost is found to be of order $O(n)$, which provides an advantage over the existing schemes having quantum cost of exponential order.