Optimal cloning of unitary transformations

Physical Review Letters, 2008

After proving a general no-cloning theorem for black boxes, we derive the optimal universal cloning of unitary transformations, from one to two copies. The optimal cloner is realized by quantum channels with memory, and greately outperforms the optimal measure-and-reprepare cloning strategy. Applications are outlined, including two-way quantum cryptographic protocols.

Lecture Notes in Computer Science, 1999

We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum logical network. We also present network for an optimal quantum copying "machine" (transformation) which produces N + 1 identical copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copies, N. In addition, we present the machine which universaly and optimally clones states of quantum objects in arbitrary-dimensional Hilbert spaces. In particular, we discuss universal cloning of quantum registers.

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, 1996

We analyze the possibility of copying ͑that is, cloning͒ arbitrary states of a quantum-mechanical spin-1/2 system. We show that there exists a ''universal quantum-copying machine'' ͑i.e., transformation͒ which approximately copies quantum-mechanical states such that the quality of its output does not depend on the input. We also examine a machine which combines a unitary transformation and a selective measurement to produce good copies of states in the neighborhood of a particular state. We discuss the problem of measurement of the output states. ͓S1050-2947͑96͒08408-9͔

Quantum Information Processing, 2014

We demonstrate the possibility of controlling the success probability of a secret sharing protocol using a quantum cloning circuit. The cloning circuit is used to clone the qubits containing the encoded information and en route to the intended receipients. The success probability of the protocol depends on the cloning parameters used to clone the qubits. We also establish a relation between the concurrence of initially prepared state, entanglement of the mixed state received by the receivers after cloning scheme and the cloning parameters of cloning machine. * [email protected]

Physical Review A, 2003

We characterize the complete set of protocols that may be used to securely encrypt n quantum bits using secret and random classical bits. In addition to the application of such quantum encryption protocols to quantum data security, our framework allows for generalizations of many classical cryptographic protocols to quantum data. We show that the encrypted state gives no information without the secret classical data, and that 2n random classical bits are the minimum necessary for informationally secure quantum encryption. Moreover, the quantum operations are shown to have a surprising structure in a canonical inner product space. This quantum encryption protocol is a generalization of the classical one time pad concept. A connection is made between quantum encryption and quantum teleportation[1], and this allows for a new proof of optimality of 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, 2004

It is shown that any quantum operation that perfectly clones the entanglement of all maximallyentangled qubit pairs cannot preserve separability. This "entanglement no-cloning" principle naturally suggests that some approximate cloning of entanglement is nevertheless allowed by quantum mechanics. We investigate a separability-preserving optimal cloning machine that duplicates all maximally-entangled states of two qubits, resulting in 0.285 bits of entanglement per clone, while a local cloning machine only yields 0.060 bits of entanglement per clone. PACS numbers: 03.67.-a, 03.65.-w

Physical Review A, 2012

We present the first experimental implementation of a multifunctional optimal quantum cloner. Previous implementations have always been designed to optimize the cloning procedure with respect to one single type of a priori information about the cloned state. In contrast, our "all in one" implementation is optimal for several prominent regimes such as universal cloning, phase-covariant cloning and also, the first ever realized mirror phase-covariant cloning, when the square of the expected value of Pauli's Z operator is known in advance. In all these regimes the experimental device yields clones with almost maximum achievable average fidelity (97.5% of theoretical limit). Our device has a wide range of possible applications in quantum information processing especially in quantum communication. For instance, one can use it for incoherent and coherent attacks against a variety of cryptographic protocols including the BB84 protocol of quantum key distribution through the Pauli damping channels. It can be also applied as a state-dependent photon multiplier in practical quantum networks. PACS numbers: 42.50.Ex, 03.67.Lx