Multiparty secret sharing of quantum information using and identifying Bell states

Zhang, Z. J.; Yang, Jie; Man, Zhong‐Xiao; Li, Yong

doi:10.1140/epjd/e2005-00029-5

Cited by 131 publications

(60 citation statements)

References 25 publications

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“…Applying the theory of quantum mechanics in the field of information, many interesting developments have been produced in last decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], such as quantum teleportation [1], quantum dense coding [2], quantum secret sharing [3], remote state preparation [4], and so on. Quantum teleportation was first proposed by Bennett et al [1] in 1993.…”

Section: Introductionmentioning

confidence: 99%

Symmetric Remote Two-Qubit Preparation via Positive Operator-Valued Measure

Wang

Yang²

2010

JAMS

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Abstract. We present a novel tripartite scheme for remotely preparing an arbitrary two-qubit state with two three-qubit entanglements. By using a proper positive operator-valued measure (POVM), it is shown that the remote two-qubit preparation can be realized in either distant ministrant's place in a probabilistic manner via their collaboration. We also explore its applications to six special ensembles of state in detail. The extensive investigations show that the remote preparation can be achieved with higher probability provided that the prepared state belongs to the six special ensembles.

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Section: Introductionmentioning

confidence: 99%

Symmetric Remote Two-Qubit Preparation via Positive Operator-Valued Measure

Wang

Yang²

2010

JAMS

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“…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.…”

mentioning

confidence: 99%

“…The 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.…”

mentioning

confidence: 99%

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

Xiao-Fei¹

2009

Int J Theor Phys

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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 ( )

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“…Mor and Horodecki [2] used POVM to the problems of teleportation, which has been studied widely [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] and has a number of useful applications in quantum information and quantum computation [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]. It was shown that a perfect conclusive teleportation can be obtained with any pure entangled states.…”

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confidence: 99%

An Implementation of a Positive Operator Valued Measure

Yan

Gao

2007

Chinese Phys. Lett.

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An implementation of the positive operator valued measure (POVM) is given. By using this POVM one can realize the probabilistic teleportation of an unknown two-particle state.As a special case of the general measurement formalism, positive operator valued measure (POVM) provides the simplest means by which one can study general measurement statistics, without the necessity for knowing the postmeasurement state. They are viewed as a mathematical convenience that sometimes gives extra insight into quantum measurements [1]. Some of the time, one can perform a POVM to distinguish the states, but never make an error of mis-identification. Of course this infallibility comes at the price that sometimes one obtains no information about the identity of the state [1].Mor and Horodecki [2] used POVM to the problems of teleportation, which has been studied widely [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] and has a number of useful applications in quantum information and quantum computation [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]. It was shown that a perfect conclusive teleportation can be obtained with any pure entangled states. Recently, we proposed a scheme [25] for probabilistic teleportation of an unknown two-particle state with a four-particle pure entangled state and the POVM. In Ref.[25] we only gave the POVM operators, but did not present the concrete implementation of the POVM. In this Letter we will study this problem in details, especially an implementation of the POVM will be presented.The optimal POVM chosen by us in Ref.[25] contains five elements (here we use a simple form, there is only a little difference between them)whereI is an identity operator, α, β, γ, δ are nonzero real numbers with 1 α 2 + 1 β 2 + 1 γ 2 + 1 δ 2 = 1, q is a coefficient relating to α, β, γ, and δ such that 1 ≤ 1 q 2 ≤ 4, and makes P 5 to be a positive operator. Of course if we choose q 2 = µ 2 4 , where µ 2 is the smallest one in the set {α 2 , β 2 , γ 2 , δ 2 }, we can obtain the highest probability of successful teleportation of an unknown two-particle state [25].In order to implement this POVM, we construct a unitary operation U , which satisfies U |ψ |000 = P 1 |ψ |000 + P 2 |ψ |001 + P 3 |ψ |010 + P 4 |ψ |011 + P 5 |ψ |100for an arbitrary two-particle state |ψ . Here the last three qubits are the auxiliary particles. When the unitary operator U has been performed, we can measure the auxiliary particles and obtain the measurement result. It is easy to see that if U is a unitary operator such that

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Multiparty secret sharing of quantum information using and identifying Bell states

Cited by 131 publications

References 25 publications

Symmetric Remote Two-Qubit Preparation via Positive Operator-Valued Measure

Symmetric Remote Two-Qubit Preparation via Positive Operator-Valued Measure

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

An Implementation of a Positive Operator Valued Measure

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