Assisted cloning of an unknown two-particle entangled state

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We present two schemes for perfect cloning unknown two-qubit and general twoqubit entangled states with assistance from two state preparers, respectively. In the schemes, the sender wish to teleport an unknown two-qubit (or general two-qubit) entangled state which from two state preparers to a remote receiver, and then create a perfect copy of the unknown state at her place. The schemes include two stages. The first stage of the schemes requires usual teleportation. In the second stage, to help the sender realize the quantum cloning, two state preparers perform two-qubit projective measurements on their own qubits which from the sender, then the sender can acquire a perfect copy of the unknown state. To complete the assisted cloning schemes, several novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two state preparers collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubit respectively, the sender can create a copy of the unknown state by means of some appropriate unitary operations. The advantage of the present schemes is that the total success probability for assisted cloning a perfect copy of the unknown state can reach 1.Keywords Assisted cloning · Teleportation · Two-qubit entangled state · General two-qubit entangled state · Two-qubit projective measurement IntroductionEntanglement is the most fascinating feature of quantum mechanics and plays a central role in quantum information processing such as quantum teleportation [1], quantum dense coding [2], quantum cryptography [3], quantum secret sharing [4], and so on. Entanglement is also related to quantum cloning. Different from classical information, an unknown quantum state cannot be cloned exactly because of the on-cloning theorem [5]. However, quantum

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confidence: 99%

Deterministic Joint Assisted Cloning of Unknown Two-Qubit Entangled States

Zhan

2011

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“…Along the line of Zhan's protocols [35], I present in detail my generalized protocols as follows. Let us first consider the case that maximally-entangled two-qubit pairs are taken as quantum channel.…”

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confidence: 99%

“…Case II: α, β, γ and δ satisfy η = 1 In this case, if Victor's measurement result is |ξ 4 12 , then the collapsed state of qubits 3 and 5, according to the equation 11, is α|00 35 35 (except for a overall trivial factor). With Victor's help, Alice can also copy the original state in her qubits 3 and 5 by performing the local unitary operation…”

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confidence: 99%

“…Then if the state |ξ 1 12 is measured, under Victor's help, Alice knows the state of her qubits 3 and 5, except for a overall trivial factor, will be left in β * |00 35 35 .It can also be reexpressed as…”

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confidence: 99%

“…To summarize, by using the POVM instead of the more commonly used collective unitary operation in the quantum teleportation process, I have successfully generalized the protocols proposed by Zhan recently [35] to clone or anti-clone an arbitrary unknown two-qubit entangled state. With the assistance of the unknown-state preparer Victor, the present protocols can produce perfect copy or orthogonal-complement copies of an arbitrary unknown two-qubit entangled state via classical and quantum channels.…”

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confidence: 99%

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Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-qubit Entangled State via Positive Operator-valued Measure

Xiao-Fei¹

2009

By using positive operator-valued measure (POVM) instead of the more commonly used collective unitary operation in the quantum teleportation process, Zhan's scheme (Zhan in Phys. Lett. A 336:317, 2005) is generalized to treat an arbitrary (not a special class of ) unknown two-qubit entangled state. Generally speaking, conditioned on Victor's classical message, Alice can create either a copy or an orthogonal-complement copy of the original state. However, it is shown that Alice's perfect clone can be realized with higher probability or even in a deterministic manner via an appropriate unitary operation provided that the state to be cloned is chosen from six special ensembles.Keywords Quantum cloning · Arbitrary two-qubit entangled state · Two-qubit projective measurement · Positive operator-valued measure · Unitary operationThe principles of quantum mechanics supplied many interesting application in the field of information in the last decade, such as quantum computer [1, 2], quantum cryptography [2-5], quantum teleportation [6], quantum secret sharing (QSS) [7][8][9][10][11][12][13][14], and so on. One of the greatest differences between classical and quantum information is that while classical information can be copied perfectly, quantum cannot. In particular, one can not create a duplicate of an arbitrary qubit without destroying the original one [15]. This follows from the no-cloning theorem of Wootters and Zurek [16] (see also [17,18]). However, quantum cloning or approximate cloning is necessary in some quantum information processes [19]. Hence, in literatures various approximate cloning machines have been proposed [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], which operate either in a deterministic or probabilistic way. Very recently Zhan [35] has proposed two quantum cloning protocols. In his first protocol, two maximally entangled two-qubit states (i.e., Bell states) are taken as quantum channel, and a perfect clone of a special class of unknown two-qubit entangled state (i.e., α|00 + β|11 with |α| 2 + |β| 2 = 1) or implementation of its complement state is realized with assistance offered by the unknown N. Xiao-Fei ( )

Scheme for Cloning an Unknown Entangled State with Assistance via Non-maximally Entangled Cluster States

Hou

Shou-Hua

2008

We propose a scheme for cloning unknown two-particle entangled state and its orthogonal complement state with assistance from a state preparer. Two stages were included in this scheme. The first stage requires usual teleportation by using a one-dimensional nonmaximally four-particle cluster state as quantum channel, after Alice's (the state sender) Bell measurement, Bob (the state receiver) can get the original state with certain probability. In the second stage, after having received Victor's (the state preparer) classical message, the perfect copies and complement copies of an unknown state can be produced in Alice's place, the probability of Alice to get the original state or its orthogonal complement state are calculated. Assisted cloning of an arbitrary unknown two-particle entangled state is discussed in the latter scheme.