Quantum copying: Beyond the no-cloning theorem

Physics Letters, Section A: General, Atomic and Solid State Physics, 2002

It was shown that the copying quality of the Wootters-Zurek quantum copying machine depends on the input states. So Buzek and Hillery proposed the notion of universal copying machine. A universal machine is a quantum copier whose copying quality is independent of the input states. Buzek and Hillery further introduced a class of universal copying machines. In this short Letter, we establish a sufficient and necessary condition for a general copying machine to be universal. This condition will degenerate to the Buzek and Hillery's original one when we use it to analyze the Buzek and Hillery machines. On the other hand, this result enables us to find some new universal quantum-copying machines, and it also helps us to derive some interesting properties of universal machines.

Physical Review Letters, 1998

We present the universal cloning transformation of states in arbitrary-dimensional Hilbert spaces. This unitary transformation attains the optimal fidelity of cloning as specified by Werner [Phys. Rev. A 58, 1827 (1998)]. With this cloning transformation, pure as well as impure states can be optimally copied, and the quality of the copies does not depend on the state being copied. We discuss the properties of quantum clones. In particular, we show that in the limit of high dimension the fidelity of clones does not converge to zero but attains the limit 1͞2. We also show that our cloning transformation is most suitable for cloning of entanglement. [S0031-9007(98)07854-5]

Physical Review A, 1998

We establish the best possible approximation to a perfect quantum cloning machine which produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a novel teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two non-orthogonal states, discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive a new upper bound on the quantum capacity of the depolarizing quantum channel.

Physical Review A, 2001

We study measurements on various subsystems of the output of a universal 1 → 2 cloning machine, and establish a correspondence between these measurements at the output and effective measurements on the original input. We show that one can implement sharp effective measurement elements by measuring only two out of the three output systems. Additionally, certain complete sets of sharp measurements on the input can be realised by measurements on the two clones. Furthermore, we introduce a scheme that allows to restore the original input in one of the output bits, by using measurements and classical communication-a protocol that resembles teleportation.

Physical Review Letters, 1998

We derive a tight upper bound for the fidelity of a universal N → M qubit cloner, valid for any M ≥ N , where the output of the cloner is required to be supported on the symmetric subspace. Our proof is based on the concatenation of two cloners and the connection between quantum cloning and quantum state estimation. We generalise the operation of a quantum cloner to mixed and/or entangled input qubits described by a density matrix supported on the symmetric subspace of the constituent qubits. We also extend the validity of optimal state estimation methods to inputs of this kind. 03.65.Bz, 03.67.-a

Physical Review A, 1997

We present a network consisting of quantum gates which produces two imperfect copies of an arbitrary qubit. The quality of the copies does not depend on the input qubit. We also show that for a restricted class of inputs it is possible to use a very similar network to produce three copies instead of two. For qubits in this class, the copy quality is again independent of the input and is the same as the quality of the copies produced by the two-copy network.

Physical Review A, 2011

We analyze quantum algorithms for cloning of a quantum measurement. Our aim is to mimic two uses of a device performing an unknown von Neumann measurement with a single use of the device. When the unknown device has to be used before the bipartite state to be measured is available we talk about 1 → 2 learning of the measurement, otherwise the task is called 1 → 2 cloning of a measurement. We perform the optimization for both learning and cloning for arbitrary dimension of the Hilbert space. For 1 → 2 cloning we also propose a simple quantum network that realizes the optimal strategy.

Physical Review A, 2008

The fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed. We illustrate this interesting point by proposing and demonstrating the superior cloning of coherent states with prior partial information. More specifically, we propose two simple transformations that under the Gaussian assumption optimally clone symmetric Gaussian distributions of coherent states as well as coherent states with known phases. Furthermore, we implement for the first time near-optimal state-dependent cloning schemes relying on simple linear optics and feedforward.

2016

Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: "Is there an optimal quantum cloning machine?" Buzek and Hillery answer to this question and construct their famous B-H quantum cloning machine. The B-H machine clones state of an arbitrary single qubit in optimal manner and hence it is universal. Generalizing this machine for two-qubit system is straightforward, but this procedure does not preserve quantum correlation existing in bipartite state in optimal manner and also, during this procedure, this machine loses its universality and becomes a state-dependent cloning machine. In this paper we propose an optimal universal local quantum state cloner for two qubit systems. Also we present two classes of state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement ...

Physical Review Letters, 2005

When prior partial information about a state to be cloned is available, it can be cloned with a fidelity higher than that of universal quantum cloning. We experimentally verify this intriguing relationship between the cloning fidelity and the prior information by reporting the first experimental optimal quantum state-dependent cloning, using nuclear magnetic resonance techniques. Our experiments may further have important implications into many quantum information processing protocols.