Quantum cloning in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>dimensions

Zanardi, Paolo

doi:10.1103/physreva.58.3484

Cited by 38 publications

(28 citation statements)

References 8 publications

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“…In d = 2, this machine simply reduces to the original universal cloning machine [5], with η = 2 3 or F = 5 6 . This machine is proved to be optimal in that it produces maximal fidelity considering its requirements [9,10,11,12,13]. It can be justified that symmetry of the outputs is a consequence of equality of the coefficients of the terms |ij AB |j X and |ji AB |j X in Eq.…”

Section: Universal Asymmetric Cloning Machinementioning

confidence: 99%

“…However, extension to triplicators is also straightforward. The question of how well one can design an approximate duplicator of a qubit (or qudit), provided that the qualities of the two outputs be independent of the input states, has been investigated by Bužek and Hillery [5,6] and the others [7,8,9,10,11,12,13].…”

Section: Universal Asymmetric Cloning Machinementioning

confidence: 99%

“…For example in BB84 protocol [4] there is a link between optimal cloning of equatorial states and optimal eavesdropping attack. There have been extensive studies on this subject that illuminate some aspects of quantum cloning [5,6,7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

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Separability in asymmetric phase-covariant cloning

2005

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Here, asymmetric phase-covariant quantum cloning machines are defined and trade-off between qualities of their outputs and its impact on entanglement properties of the outputs are studies. In addition, optimal families among these cloners are introduced and also their entanglement properties are investigated. An explicit proof of optimality is presented for the case of qubits, which is based on the no-signaling condition. Our optimality proof can also be used to derive an upper bound on trade-off relations for a more general class of optimal cloners which clone states on a specific orbit of the Bloch sphere. It is shown that the optimal cloners of the equatorial states, as in the case of symmetric phase-covariant cloning, give rise to two separable clones, and in this sense these states are unique. For these cloners it is shown that total output is of GHZ-type.

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Section: Universal Asymmetric Cloning Machinementioning

confidence: 99%

Section: Universal Asymmetric Cloning Machinementioning

confidence: 99%

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Separability in asymmetric phase-covariant cloning

2005

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“…Besides the usefulness of this cloning machine for the quantum cloning task, the result presented here is also interesting. We know the BEM bound can be achieved for identical pure input states by Werner [8] and Keyl and Werner [9] (WKW) cloning machine, see also [10]. For arbitrary states in symmetric subspace which include the identical pure states as a special case, intuitively, this bound cannot be achieved since compared with pure states case, we know less about the input.…”

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confidence: 99%

Quantum cloning of mixed states in symmetric subspaces

Fan¹

2003

Phys. Rev. A

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Quantum computation and information project, ERATO, Japan Science and Technology Corporation, Daini Hongo White Building 201, Hongo 5-28-3, Bunkyo-ku, Tokyo 113-0033, Japan.Quantum cloning machine for arbitrary mixed states in symmetric subspace is proposed. This quantum cloning machine can be used to copy part of the output state of another quantum cloning machine and is useful in quantum computation and quantum information. The shrinking factor of this quantum cloning achieves the well-known upper bound. When the input is identical pure states, two different fidelities of this cloning machine are optimal.A quantum state cannot be cloned exactly because of the no-cloning theorem [1]. However, quantum cloning approximately (or probablisticaly) is necessary in quantum computation and quantum information [2]. Suppose we have the following task: we have a pure unknown quantum state in 2-level system (qubit) |Ψ . We need one copy of this quantum state to perform one quantum computation. But we do not need it to be exactly the original one. A copy of |Ψ with fidelity of at least 7/9 can give a reliable result. And also we need another 3 identical quantum states each with the fidelity of at least 79/108 to perform another reliable quantum computation. If the fidelities of the quantum states are less than the demanding fidelities, the quantum computation will not be reliable any more. This is certainly a simple and rather practical quantum cloning task. However, we still cannot reach this simple goal by the present available optimal quantum cloning machines.Let's next analyze why the present available quantum cloning machines fail to do this work. 1, First we try to use the 1 to 4 optimal quantum cloning machine proposed by Gisin and Massar [3] to do this work. By this cloning machine, we can copy |Ψ to 4 identical quantum states each with fidelity 3/4 which is larger than 79/108 but less than 7/9. That means we can obtain a reliable result in the second quantum computation but we cannot have a reliable result in the first quantum computation. 2, We may use first the 1 to 2 cloning machine which is proposed by Buzek and Hillery [4,5]. With one output state doing the first quantum computation, then we use another quantum state as input and use the 1 to 3 Gisin-Massar cloning machine to create another 3 identical quantum states. One can find the quantum state of the first cloning machine can achieve the fidelity 5/6 which is better than the demanding fidelity 7/9. However, the 3 identical quantum states can only achieve the fidelity 37/54 which is lower than the demanding fidelity. So, we cannot finish our task by using this method. 3, One is perhaps tempted to use Cerf's asymmetric quantum cloning machine [6] to do this work. The advantage of using Cerf's asymmetric cloning machine is that we can let one quantum state achieve the fidelity 7/9 while another one still has the optimal fidelty since this cloning machine achieve the bound of the no-cloning theorem proposed by Cerf. Then we use the Gisin-Massar 1 to 3 clonin...

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“…In the last few years, much progress has been made in analyzing the optimal cloning of different systems: a 1 → 2 universal cloning machine for qubits [11], a 1 → 2 symmetric cloner for d-level systems [12], an N → M symmetric cloner for qubits (a machine that takes as input N identical qubits and generates at the output M > N copies) [13,14], and an N → M symmetric cloner for d-level systems [15,16,17,18]. While a symmetric machine produces identical output states, the 1 → 2 asymmetric cloner of qubits proposed by Cerf generates two output states emerging from two different Pauli channels [19].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric quantum telecloning ofd-level systems and broadcasting of entanglement to different locations using the “many-to-many” communication protocol

Ghiu

2003

Phys. Rev. A

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We propose a generalization of quantum teleportation: the so-called many-to-many quantum communication of the information of a d-level system from N spatially separated senders to M > N receivers situated at different locations. We extend the concept of asymmetric telecloning from qubits to d-dimensional systems. We investigate the broadcasting of entanglement by using local 1 → 2 optimal universal asymmetric Pauli machines and show that the maximal fidelities of the two final entangled states are obtained when symmetric machines are applied. Cloning of entanglement is studied using a nonlocal optimal universal asymmetric cloning machine and we show that the symmetric machine optimally copies the entanglement. The "many-to-many" teleportation scheme is applied in order to distribute entanglement shared between two observers to two pairs of spatially separated observers.

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Quantum cloning inddimensions

Cited by 38 publications

References 8 publications

Separability in asymmetric phase-covariant cloning

Separability in asymmetric phase-covariant cloning

Quantum cloning of mixed states in symmetric subspaces

Asymmetric quantum telecloning ofd-level systems and broadcasting of entanglement to different locations using the “many-to-many” communication protocol

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