Entangled Cloning of Stabilizer Codes and Free Fermions

TL;DR

This paper introduces a method to generate entangled clones of stabilizer codes and free fermion ground states, enabling controlled entanglement and transformations without physical replication, with potential applications in quantum simulation.

Contribution

It provides a novel protocol for creating entangled clones of stabilizer codes and free fermion states, allowing tunable entanglement and state transformations.

Findings

Exact entangled clones can be generated for stabilizer codes.

The protocol enables simulation of Hamiltonian transformations via entanglement.

Potential implementation in superconducting qubits or ultracold atoms.

Abstract

Though the no-cloning theorem [1] prohibits exact replication of arbitrary quantum states, there are many instances in quantum information processing and entanglement measurement in which a weaker form of cloning may be useful. Here, I provide a construction for generating an "entangled clone" for a particular but rather expansive and rich class of states. Given a stabilizer code or free fermion Hamiltonian, this construction generates an exact entangled clone of the original ground state, in the sense that the entanglement between the original and the exact copy can be tuned to be arbitrarily small but finite, or large, and the relation between the original and the copy can also be modified to some extent. For example, this work focuses on generating time-reversed copies of stabilizer codes and particle-hole transformed ground states of free fermion systems, although untransformed clones can also be generated. The protocol leverages entanglement to simulate a transformed copy of the Hamiltonian without having to physically implement it and can potentially be realized in superconducting qubits or ultracold atomic systems.