Optimal quantum cloning and universal NOT without quantum gates

Physical Review Letters, 2000

We show that optimal universal quantum cloning can be realized via stimulated emission. Universality of the cloning procedure is achieved by choosing systems that have appropriate symmetries. We first discuss a scheme based on stimulated emission in certain three-level systems, e.g. atoms in a cavity. Then we present a way of realizing optimal universal cloning based on stimulated parametric down-conversion. This scheme also implements the optimal universal NOT operation.

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 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]

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 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

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

Science, 2002

Although perfect copying of unknown quantum systems is forbidden by the laws of quantum mechanics, approximate cloning is possible. A natural way of realizing quantum cloning of photons is by stimulated emission. In this context the fundamental quantum limit to the quality of the clones is imposed by the unavoidable presence of spontaneous emission. In our experiment a single input photon stimulates the emission of additional photons from a source based on parametric downconversion. This leads to the production of quantum clones with near optimal fidelity. We also demonstrate universality of the copying procedure by showing that the same fidelity is achieved for arbitrary input states.

Physical Review Letters, 2005

A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is only limited by detection inefficiencies. Experimentally we achieved a cloning fidelity of about 65%, which almost touches the optimal value of 2/3. PACS numbers: 03.67. Hk, 03.65.Ta, 42.50.Lc According to the basic laws of quantum mechanics, an unknown nonorthogonal quantum state cannot be copied exactly . In other words, it would be an impossible task to devise a process that produces perfect clones of an arbitrary quantum state. However, a physical realization of a quantum cloning machine with less restrictive requirements to the quality of the clones is possible. Such a quantum cloning machine was first considered in a seminal paper by Buzek and Hillery [3] where they went beyond the no-cloning theorem by considering the possibility of producing approximate clones for qubits. These considerations were later extended to the finite-dimensional regime [4] and finally to the continuous variable (CV) regime . This extension is stimulated by the relative ease in preparing and manipulating quantum states in the CV regime as well as the unconditionalness: Every prepared state is used in the protocols. Governed by these motivations many quantum protocols have been experimentally realized in this regime .

Physical Review A, 2012

We study an initially inverted three-level atom in the lambda configuration embedded in a waveguide, interacting with a propagating single-photon pulse. Depending on the temporal shape of the pulse, the system behaves either as an optimal universal cloning machine, or as a highly efficient deterministic source of maximally entangled photon pairs. This quantum transistor operates over a wide range of frequencies, and can be implemented with today's solid-state technologies.

Physical Review A, 2012

We consider a sequential implementation of the optimal quantum cloning machine of Gisin and Massar and propose optimization protocols for experimental realization of such a quantum cloner subject to the real-life restrictions. We demonstrate how exploiting the matrix-product state (MPS) formalism and the ensuing variational optimization techniques reveals the intriguing algebraic structure of the Gisin-Massar output of the cloning procedure and brings about significant improvements to the optimality of the sequential cloning prescription of Delgado et al [Phys. Rev. Lett. 98, 150502 (2007)]. Our numerical results show that the orthodox paradigm of optimal quantum cloning can in practice be realized in a much more economical manner by utilizing a considerably lesser amount of informational and numerical resources than hitherto estimated. Instead of the previously predicted linear scaling of the required ancilla dimension D with the number of qubits n, our recipe allows a realization of such a sequential cloning setup with an experimentally manageable ancilla of dimension at most D = 3 up to n = 15 qubits. We also address satisfactorily the possibility of providing an optimal range of sequential ancilla-qubit interactions for optimal cloning of arbitrary states under realistic experimental circumstances when only a restricted class of such bipartite interactions can be engineered in practice.