Encrypted Qubits can be Cloned

Abstract

We show that encrypted cloning of unknown quantum states is possible. Any number of encrypted clones of a qubit can be created through a unitary transformation, and each of the encrypted clones can be decrypted through a unitary transformation. The decryption of an encrypted clone consumes the decryption key, i.e., only one decryption is possible, in agreement with the no-cloning theorem. Encrypted cloning represents a new paradigm that provides a form of redundancy, parallelism or scalability where direct duplication is forbidden by the no-cloning theorem. For example, a possible application of encrypted cloning is to enable encrypted quantum multi-cloud storage.

Figures (2)

• Figure 1: The protocol for $n=2$. Qubits whose reduced state is maximally mixed are represented by spheres displaying fluctuations. The initial maximal mixedness of $S_1$ and $S_2$, which stems from their being prepared in Bell states with $N_1$ and $N_2$ respectively, provides the quantum noise for the encryption. $N_1$ and $N_2$ keep a record of this quantum noise and can, therefore, later be used to de-noise or decrypt either $S_1$ or $S_2$. Crucially, the decryption machine consumes $N_1$ and $N_2$, so that only one decryption can be performed. Therefore, only one unencrypted version of the original state of $A$ can exist at a time, which enables consistency with the no-cloning theorem.
• Figure 2: Plot for coherent information given in Eq. \ref{['eq:formula_coh_info']}. $I(\widetilde{A}\rangle S_1N_1N_2\cdots N_n)_\rho =1$ if $t=\frac{\pi}{4}+\frac{\pi}{2}m$ for $m\in\mathbb{Z}$.