Teleportation Scheme Implementing the Universal Optimal Quantum Cloning Machine and the Universal NOT Gate

Ricci, Marco; Sciarrino, Fabio; Sias, Carlo; Martini, F. De

doi:10.1103/physrevlett.92.047901

Cited by 102 publications

(95 citation statements)

References 23 publications

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“…The cloner is called optimal when it gives the best results allowed by quantum mechanics. Moreover universal cloning (UC) should operate equally well for all possible qubit states [4][5][6][7][8]. In contrast, limiting cloning to a specific subset of qubit states, one can achieve a more precise cloning operation.…”

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Experimental linear-optical implementation of a multifunctional optimal qubit cloner

et al. 2012

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We present the first experimental implementation of a multifunctional device for the optimal cloning of one to two qubits. 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 Paulis Z operator is known in advance.In all these regimes the experimental device yields clones with almost maximum achievable aver-age 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 Bennett-Brassard 1984 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. Introduction. One of the most fundamental laws of nature, the so-called no-cloning theorem, states that an unknown quantum state cannot be perfectly copied. This fact has an imminent impact on quantum information processing. For instance, it allows designing inherently secure cryptographic protocols [1] or assures the impossibility of superluminal communication [2]. Although perfect quantum copying is impossible, one can still investigate how well such an operation can be approximated within the limits of physical laws. Despite some very intense research in this domain, many aspects of statedependent quantum cloning have not yet been fully investigated.Quantum cloning is one of the most intriguing topics in quantum physics. It is important not only because of its fundamental nature but also because of its immediate applications to quantum communications, including quantum cryptography. Similar to other important quantum information processing protocols, quantum cloning has undergone considerable development over the past two decades. The first design of an optimal cloning machine was suggested by Bužek and Hillery [3]. The cloner is called optimal when it gives the best results allowed by quantum mechanics. Moreover universal cloning (UC) should operate equally well for all possible qubit states [4][5][6][7][8]. In contrast, limiting cloning to a specific subset of qubit states, one can achieve a more precise cloning operation. A prominent example of this situation is phase-covariant cloning (PCC), where only qubit states with equal superposition of |0 and |1 are considered [9][10][11][12][13][14][15].In this Rapid Communication we address a question

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Experimental linear-optical implementation of a multifunctional optimal qubit cloner

et al. 2012

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“…Today, optimal quantum cloners are known for many different cases and scenarios [3,4]. During recent years, growing attention has been paid to the experimental implementation of quantum cloning machines and, in particular, optimal cloning of polarization states of single photons via stimulated parametric downconversion or via photon bunching on a beam splitter has been successfully demonstrated [5,6,7,8,9,10].Besides giving an insight into the fundamental limits on distribution of quantum information, the quantum cloning machines turned out to be very efficient eavesdropping attacks on the quantum key distribution protocols [11,12,13,14]. In this context one is particularly interested in the asymmetric quantum cloners that produce two copies with different fidelities.…”

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Fiber-Optics Implementation of an Asymmetric Phase-Covariant Quantum Cloner

et al. 2007

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We present the experimental realization of optimal symmetric and asymmetric phase-covariant 1 → 2 cloning of qubit states using fiber optics. State of each qubit is encoded into a single photon which can propagate through two optical fibers. The operation of our device is based on one-and two-photon interference. We have demonstrated creation of two copies of any state of a qubit from the equator of the Bloch sphere. The measured fidelities of both copies are close to the theoretical values and they surpass the theoretical maximum obtainable with the universal cloner.PACS numbers: 03.67.-a, 42.50.-p, 32.80.-t The quantum no-cloning theorem [1] lies at the heart of quantum information theory. The apparently simple observation that perfect copying of unknown quantum states is impossible has profound consequences. On the fundamental side, it prevents superluminal communication with entangled states, thereby guaranteeing the peaceful coexistence of quantum mechanics and theory of relativity. On the practical side, this theorem is behind the security of the quantum key distribution schemes which rely on the fact that any attempt to measure or copy an unknown quantum state results in the disturbance of this state. Going beyond the no-cloning theorem, Bužek and Hillery in a seminal paper introduced the concept of the universal approximate quantum cloning machine that optimally approximates the forbidden transformation |ψ → |ψ |ψ [2]. Today, optimal quantum cloners are known for many different cases and scenarios [3,4]. During recent years, growing attention has been paid to the experimental implementation of quantum cloning machines and, in particular, optimal cloning of polarization states of single photons via stimulated parametric downconversion or via photon bunching on a beam splitter has been successfully demonstrated [5,6,7,8,9,10].Besides giving an insight into the fundamental limits on distribution of quantum information, the quantum cloning machines turned out to be very efficient eavesdropping attacks on the quantum key distribution protocols [11,12,13,14]. In this context one is particularly interested in the asymmetric quantum cloners that produce two copies with different fidelities. In this way, the eavesdropper can control the trade-off between the information gained on a secret cryptographic key and the amount of noise added to the copy which is sent down the channel to the authorized receiver. While the theory of optimal asymmetric quantum copying machines is well established (see, e.g. the recent reviews [3,4]), the experimental optical realization of such machines has received considerably less attention. This might be attributed to the fact that the asymmetric cloning operations exhibit much less symmetry than the corresponding symmetric ones. To the best of our knowledge, asymmetric quantum cloning of single-photon states has been so far achieved only in a single experiment, where universal asymmetric copying of polarization states was performed by means of partial quantum teleportation [15].In...

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“…the universal optimal quantum cloning machine (UQCM) and the universal-NOT (U-NOT) gate [6]. The optimal quantum cloning machine has been experimentally realized following different approaches: by exploiting the process of stimulated emission [7,8,9], by means of a quantum network [10] and by adopting projective operators into the symmetric subspaces of many qubits [11,12,13]. The N → M UQCM transforms N input qubits in the state |φ into M output qubits, each one in the same mixed state ρ out .…”

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Implementation of optimal phase-covariant cloning machines

Sciarrino

Martini

2007

Phys. Rev. A

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The optimal phase covariant cloning machine (PQCM) broadcasts the information associated to an input qubit into a multi-qubit systems, exploiting a partial a-priori knowledge of the input state. This additional a priori information leads to a higher fidelity than for the universal cloning. The present article first analyzes different experimental schemes to implement the 1 −→ 3 P QCM . The method is then generalized to any 1 −→ M machine for odd value of M by a theoretical approach based on the general angular momentum formalism. Finally different experimental schemes based either on linear or non-linear methods and valid for single photon polarization encoded qubits are discussed.The problem of manipulating and controlling the flux of quantum information between many quantum systems has in general been tackled and solved by the theory of quantum cloning and broadcasting [1,2,3]. From a practical point of view, this feature renders the theory of cloning a fundamental tool for the analysis of the security of quantum cryptographic protocols, for the distribution of quantum information to many partners and for the transmission of information contained in a system into correlations between many systems. In spite of the fact that, for fundamental reasons, the quantum cloning and flipping operations over an unknown qubit |φ are unrealizable in their exact forms [4,5], they can be optimally approximated by the corresponding universal quantum machines, i.e. the universal optimal quantum cloning machine (UQCM) and the universal-NOT (U-NOT) gate [6]. The optimal quantum cloning machine has been experimentally realized following different approaches: by exploiting the process of stimulated emission [7,8,9], by means of a quantum network [10] and by adopting projective operators into the symmetric subspaces of many qubits [11,12,13]. The N → M UQCM transforms N input qubits in the state |φ into M output qubits, each one in the same mixed state ρ out . The quality of the copies is quantified by the fidelity parameter FNot only the "universal" cloning of any unknown qubit is forbidden, but also the cloning of subsets containing non orthogonal states. This no-go theorem ensures the security of cryptographic protocols as BB84 [14]. Recently state dependent, non universal, optimal cloning machines have been investigated where the cloner is optimal with respect to a given ensemble [15]. This partial a − priori knowledge of the state allows to reach a higher fidelity than for the universal cloning. The simplest and most relevant case is represented by the cloning covariant under the Abelian group U (1) of phase rotations, the so called "phase-covariant" cloning. There the information is encoded in the phase φ i of the input qubit belonging to any equatorial plane i of the corresponding Bloch sphere.In this context the general state may be expressed as:. Precisely, in the general case the N → M phase covariant cloning map C N M satisfies the following covariance relationThere the σ i Pauli operator identifies the set of input state...

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Teleportation Scheme Implementing the Universal Optimal Quantum Cloning Machine and the Universal NOT Gate

Cited by 102 publications

References 23 publications

Experimental linear-optical implementation of a multifunctional optimal qubit cloner

Experimental linear-optical implementation of a multifunctional optimal qubit cloner

Fiber-Optics Implementation of an Asymmetric Phase-Covariant Quantum Cloner

Implementation of optimal phase-covariant cloning machines

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