Quantum Cloning and Processing

Miguel Orszag

Pavel Sekatski, Yelena Guryanova, Naga Bhavya Teja Kothakonda +1 more

We consider the problem of deterministically cloning quantum channels with respect to the best attainable rate and the highest quality, so-called optimal cloning. We demonstrate that cloning quantum states is, in-fact, equivalent to cloning the trash-and-replace channel and therefore the former is a special case of the more general problem. By appealing to higher-order quantum operations (quantum processes) we construct a unified framework to deal with the most general cloning tasks and establish necessary conditions for a family of channels to exhibit super-replication -- a quadratic cloning rate with vanishing error. We find that noisy phase-gate channels satisfy these conditions, and we construct the explicit super-replicating process for the task. Conversely, we find that the criteria are not met by the full set of noisy unitary gates; classical noise channels; or amplitude damping channels, whose respective cloning rates are at most linear. In this paradigm, we not only derive new results, but also refigure known ones. We derive a strong converse for state cloning, and for unitary channels we construct an alternative super-replication process to that of Dür et al. [PRL 114, 120503 (2015)] and Chiribella et al. [PRL 114, 120504 (2015)] based on a measure-and-prepare process, which allows us to establish a direct connection between optimal channel cloning and Bayesian channel estimation. Finally we give an SDP algorithm to search for optimal cloning processes and study the advantage of coherent vs measure-and-prepare protocols on concrete examples.

Qian Jun Beh, Moritz Straeter, Zeen Sun +2 more

Quantum cloning machines are essential in quantum information processing, finding applications in areas such as quantum communication and cryptographic protocols. However, the fidelity of universal quantum cloning machines diminishes as the dimension of the Hilbert space increases, resulting in significantly lower efficiency when cloning high-dimensional quantum states compared to qubits. In this study, we introduce a Hybrid Quantum Autocloning Machine (HQAM) that combines quantum autoencoding with universal quantum cloning. The core concept involves compressing a high-dimensional quantum state into a lower-dimensional effective subspace through a quantum autoencoder, conducting the cloning process within this reduced subspace, and then reconstructing the state in the original Hilbert space. Our results show that, for input states with a strong overlap with the effective qubit subspace, the HQAM achieves cloning fidelities exceeding the benchmark fidelity of direct qutrit universal cloning and approaching the optimal qubit cloning limit, while maintaining robustness under noise. These findings demonstrate that compression-assisted cloning provides a practical strategy for improving cloning performance in high-dimensional quantum systems and may enable more efficient quantum information processing protocols.

Zhi-Hao Bi, Jing-Tao Qiu, Xiao‐Dong Yu

The inherent limitations of physical processes prevent the copying of arbitrary quantum states. Furthermore, even if we only aim to clone two distinct quantum states, it remains impossible unless they are mutually orthogonal. To overcome this limitation, we propose a virtual-cloning protocol that bypasses the restrictions imposed by the quantum no-cloning theorem. Specifically, we begin by outlining the general framework for virtual cloning and deriving a necessary and sufficient criterion for the existence of a virtual operation capable of simultaneously cloning a set of states. Subsequently, through an analysis of the simulation cost of the virtual-cloning process, we demonstrate that the problem of identifying an optimal virtual-cloning protocol can be cast as a semidefinite programming problem. Finally, we establish a connection between virtual cloning and state discrimination, from which universal bounds on the optimal cloning cost are derived.