Arbitrary Three-qubit State Research Articles

Quantum state sharing of an arbitrary three-qubit state by using four sets of W-class states

A new application of the W-class state is investigated for quantum state sharing (QSTS) of an arbitrary three-qubit state. We demonstrate that four sets of W-class states can be used to realize the deterministic QSTS of an arbitrary three-qubit state based on the three-qubit von Neumann measurements and the local unitary operations. Our scheme considered here is secure against certain eavesdropping attacks.

Controlled Teleportation of an Arbitrary Three-Qubit State by Using a Genuinely Entangled Six-Qubit State and a Bell-State

A new application of the genuinely entangled six-qubit state introduced recently by Borras et al. [J. Phys. A 40:13407, 2007] is investigated for the controlled teleportation of an arbitrary three-qubit state. In our scheme, a genuinely entangled six-qubit state and a Bell-state are shared by a sender (Alice), a controller (Charlie) and a receiver (Bob). Both the sender and the controller only need to perform Bell-state measurements (BSMs), the receiver can reconstruct the arbitrary three-qubit state by performing some appropriate unitary transformations on his qubits after he knows the measured results of both the sender and the controller. This controlled teleportation scheme is deterministic.

Quantum information splitting of an arbitrary three-qubit state by using two four-qubit cluster states

A new application of the four-qubit cluster state is investigated for quantum information splitting (QIS) of an arbitrary three-qubit state. Muralidharan and Panigrahi (Phys Rev A 78:062333, 2008) argued that a four-qubit cluster state is impossible for QIS of an arbitrary two-qubit state. In this paper, we demonstrate that two four-qubit cluster states can be used to realize the deterministic QIS of an arbitrary three-qubit state by performing only the Bell-state measurements. Our scheme considered here is secure against certain eavesdropping attacks.

Quantum Teleportation and Quantum Information Splitting by Using a Genuinely Entangled Six-Qubit State

A new application of the genuinely entangled six-qubit state introduced recently by Tapiador et al. (J. Phys. A 42:415301, 2009) is investigated for the quantum teleportation of an arbitrary three-qubit state and for quantum information splitting (QIS) of an arbitrary two-qubit state. For QIS, we have shown that it can be completed perfectly with two distinct measurement methods. In our scheme, the joint Bell-state measurement and the joint multi-qubit measurement are needed. This quantum teleportation and QIS schemes are deterministic.

Joint remote preparation of an arbitrary three-qubit state

In this paper, by constructing some useful measurement bases, we first show that two senders can jointly prepare a three-qubit state of complex coefficients to a remote receiver via the shared three GHZ states. Then, the success probability can be improved by using the permutation group to classify the preparation state. Furthermore, under some different measurement bases, we propose another scheme to jointly prepare a three-qubit state of real coefficients with less restrictions. Finally, the present schemes are extended to multi-sender, and the classical communication costs of all the schemes are also calculated.

Perfect teleportation of an arbitrary three-qubit state with the highly entangled six-qubit genuine state

The perfect teleportation of an arbitrary three-qubit state with the highly entangled six-qubit genuine state introduced by Borras et al. (J. Phys. A: Math. Theor. 40 (2007) 13407) is studied. Some appropriate measuring bases the sender can take and the corresponding unitary operations the receiver should execute in terms of the sender’s measurement outcome are explicitly given. The flexibility between the measurement difficulty and the reconstruction difficulty is shown. Moreover, discussions and comparisons between our scheme and the recent incomplete scheme (Choudhury et al, J. Phys. A: Math. Theor. 42 (2009) 115303) are made.

Transformation Operator and Criterion for Perfectly Teleporting Arbitrary Three-Qubit State with Six-Qubit Channel and Bell-State Measurement

Using the method presented recently [Phys. Rev. A 77 (2008) 014306; Phys. Lett. A 369 (2007) 377], the transformation operator (TO) is explicitly given for teleporting an arbitrary three-qubit state with a six-qubit channel and Bell-state measurements. A criterion on whether such quantum teleportation can be perfectly realized is educed in terms of TO. Moreover, six instantiations on TO and criterion are concisely shown.

Quantum teleportation and state sharing using a genuinely entangled six-qubit state

The usefulness of the genuinely entangled six-qubit state that has recently been introduced by Borras et al (2007 J. Phys. A: Math. Theor. 40 13407) is investigated for the quantum teleportation of an arbitrary three-qubit state and for quantum state sharing (QSTS) of an arbitrary two-qubit state. We construct two distinct protocols for QSTS of an arbitrary two-qubit state using this state as an entangled channel. We construct 16 orthogonal four-qubit states which can lock an arbitrary two-qubit state between two parties.

Three-qubit Groverian measure

The Groverian measures are analytically computed in various types of three-qubit states. The final results are also expressed in terms of local-unitary invariant quantities in each type. This fact reflects the manifest local-unitary invariance of the Groverian measure. It is also shown that the analytical expressions for various types have correct limits to other types. For some types (type 4 and type 5) we failed to compute the analytical expression of the Groverian measure in this paper. However, from the consideration of local-unitary invariants we have shown that the Groverian measure in type 4 should be independent of the phase factor $\varphi$, which appear in the three-qubit state $|\psi \rangle$. This fact with geometric interpretation on the Groverian measure may enable us to derive the analytical expressions for general arbitrary three-qubit states in near future.

Probabilistic Controlled Teleportation of an Arbitrary Three-Qubit State

Recently Jiang et al. [Chin. Phys. Lett. 24 (2007) 1144] gave a scheme for probabilistic controlled teleportation of a triplet W state from the sender Alice to the distant receiver Bob. The m controlled qubits are shared by m(s1, s2, …, sm) spatially-separated supervisors. Based on transformation operator, we can extend to teleporting an arbitrary three-qubit state. The relation between the transformation operators and the Bob's unitary transformation is also obtained.

Stringy black holes and the geometry of entanglement

Recently striking multiple relations have been found between pure state two- and three-qubit entanglement and extremal black holes in string theory. Here we add further mathematical similarities which can be both useful in string and quantum information theories. In particular, we show that finding the frozen values of the moduli in the calculation of the macroscopic black-hole entropy in the $STU$ model is related to finding the canonical form for a pure three-qubit entangled state defined by the dyonic charges. In this picture the extremization of the BPS mass with respect to moduli is connected to the problem of finding the optimal local distillation protocol of a GHZ state from an arbitrary three-qubit pure state. These results and a geometric classification of $STU$ black holes, BPS and non-BPS can be described in the elegant language of twistors. Finally an interesting connection between the black-hole entropy and the average real entanglement of formation is established.