Xiansong Liu

Deterministic single-qubit operation sharing with five-qubit cluster state

Perfect sharing of arbitrary single-qubit operation (PSASQO) with shared entanglements and LOCC is focused. A symmetric three-party PSASQO scheme is put forward by utilizing the five-qubit cluster state proposed by Briegel and Raussendorf (Phys Rev Lett 86:910, 2001). Some concrete discussions on the scheme are made, including its important features, the essential role of the quantum channel, its direct generalization to more-party cases, the problem of entanglement structure and its application perspective in some peculiar quantum scenario as well as its security analysis. Particularly, the experimental feasibilities of the scheme and its generalizations are demonstrated, i.e., showing the employed unitary operations are local and accessible single-qubit Pauli and two-qubit control NOT operations according to nowaday experimental techniques.

Quantum operation sharing with symmetric and asymmetric W states

Two tripartite schemes for sharing a single-qubit operation on a remote target state are proposed with symmetric and asymmetric W states, respectively. They are treated and compared from the aspects of quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that the first scheme is better than the second one. In particular, the sharing can be achieved probabilistically with the first scheme while deterministically with the second one.

GENERALIZED THREE-PARTY QUBIT OPERATION SHARING

Two three-party schemes of qubit operation sharing proposed by Zhang and Cheung [J. Phys. B44 (2011) 165508] are generalized by utilizing partially entangled states as quantum channels instead of maximally entangled ones. Their quantum and classical resource consumptions, necessary-operation complexities, success probabilities and efficiencies are calculated and compared with each other. Moreover, it is revealed that the success probabilities are completely determined by the shared entanglement.

REVISITING NASERI'S SECURE QUANTUM SEALED-BID AUCTION

The secure quantum sealed-bid auction protocol [Mosayeb Naseri, Opt. Commun.282 (2009) 1939] is revisited. It is found that, utilizing intercept-measure-resend attacks, any evil bidder can make the auction aborted without being detected by the auctioneer. Further, if the evil bidder succeeds to be the first bidder, then he/she can win conclusively in the auction. To prevent such attacks, some defence strategies are adopted in the qubit distribution stage and the channel security check stage respectively and the original protocol is therefore modified somewhat.

Shared quantum control via sharing operation on remote single qutrit

Two qubit-operation-sharing schemes (Zhang and Cheung in J. Phys. B 44:165508, 2011) are generalized to the qutrit ones. Operations to be shared are classified into three different classes in terms of different probabilities (i.e, 1/3, 2/3 and 1). For the latter two classes, ten and three restricted sets of operations are found out, respectively. Moreover, the two generalized schemes are amply compared from four aspects, namely, quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the second scheme is overall more optimal than the first one as far as three restricted sets of operations are concerned. Moreover, the experimental feasibility of our schemes is confirmed with respect to the nowaday technique.

SYMMETRIC AND PROBABILISTIC MULTIPARTY REMOTE STATE PREPARATION VIA THE POSITIVE-OPERATOR-VALUED MEASURE

We present a tripartite scheme for a preparer to remotely prepare an arbitrary single-qubit state in either distant ministrants place by using a GHZ-type state. After the preparers single-qubit state projective measurement, by performing a proper positive operator-valued measure, one ministrant can construct the preparers state in a probabilistic manner with the other ministrants assistance. Furthermore, we show that the remote state preparation can be achieved with a higher probability provided that the prepared state belongs to two special ensembles. Finally, we sketch the generalization of the tripartite scheme to a multiparty case.

Analytic expressions of quantum correlations in qutrit Werner states

Quantum correlations in qutrit Werner states are extensively investigated with five popular methods, namely, original quantum discord (OQD) (Ollivier and Zurek in Phys Rev Lett 88:017901, 2001), measurement-induced disturbance (MID) (Luo in Phys Rev A 77:022301, 2008), ameliorated MID (AMID) (Girolami et al. in J Phys A Math Theor 44:352002, 2011), relative entropy (RE) (Modi et al. in Phys Rev Lett 104:080501, 2010) and geometric discord (GD) (Dakić et al. in Phys Rev Lett 105:190502, 2010). Two different analytic expressions of quantum correlations are derived. Quantum correlations captured by the former four methods are same and bigger than those obtained via the GD method. Nonetheless, they all qualitatively characterize quantum correlations in the concerned states. Moreover, as same as the qubit case, there exist quantum correlations in separable qutrit Werner states, too.

Deterministic tripartite sharing of eight restricted sets of single-qubit operations with two Bell states or a GHZ state

Two tripartite schemes with a pair of Bell states and a Greenberger–Horne–Zeilinger (GHZ) state respectively have been proposed recently by Zhang and Cheung for remotely sharing two restricted sets of operations in a deterministic manner [J. Phys. B 44 (2011) 165508]. In this paper, we generalize the schemes with the same quantum channels so that another six restricted sets of operations can be shared deterministically, too. Features about scheme security, sharer symmetry, fulfillment determinacy and experimental feasibility are discussed and revealed. Moreover, some comparisons are also made from the aspects of quantum and classical resource consumption, necessary operation complexity and efficiency.

Generalized three-party sharing of operations on remote single qutrit

Two three-party schemes are put forward for sharing quantum operations on a remote qutrit with local operation and classical communication as well as shared entanglements. The first scheme uses a two-qutrit and three-qutrit non-maximally entangled states as quantum channels, while the second replaces the three-qutrit non-maximally entangled state with a two-qutrit. Both schemes are treated and compared from the four aspects of quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the latter is overall more optimal than the former as far as a restricted set of operations is concerned. In addition, comparisons of both schemes with other four relevant ones are also made to show their two features, including degree generalization and channel-state generalization. Furthermore, some concrete discussions on both schemes are made to expose their important features of security, symmetry and experimental feasibility. Particularly, it is revealed that the success probabilities and intrinsic efficiencies in both schemes are completely determined by the shared entanglement.

A NOTE ON "SPLITTING FOUR ENSEMBLES OF TWO-QUBIT QUANTUM INFORMATION VIA THREE EINSTEIN–PODOLSKY–ROSEN PAIRS"

Enlightened by the novel idea in recent literature, we improve the tripartite quantum scheme to be a more economical and efficient one for splitting any two-qubit state in the four specific ensembles with only two Einstein–Podolsky–Rosen pairs as quantum channels.