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Journal of the Optical Society of America B

Quantum information splitting and open-destination teleportation using decomposable multipartite quantum channel part 1: theory

Parminder S. Bhatia

Published Apr 4, 2014• 2 citations
Publisher

Abstract

The theory of an experimentally feasible four-partite scheme for splitting and open-destination teleportation of an arbitrary two-qubit state is presented. In this scheme, the quantum channel is provided by a pair of four-qubit generalized (G) Bell-states, which are decomposable. We show that not all possible distributions of entangled qubits to four communicating parties result in successful open-destination teleportation. We theoretically prove that two Bell-state measurements performed by a sender result in splitting, distributing, and locking the two-qubit state among three different receivers. The complete details of the procedure for unlocking the shared two-qubit state and eventually regenerating it at the location of any one of the three receiving stations is theoretically analyzed. This unlocking and regeneration procedure consists of local operations and classical communication (LOCC) performed by the remaining two receivers.

DOI
10.1364/josab.31.000972

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The theory of an experimentally feasible four-partite scheme for splitting and open-destination teleportation of an arbitrary two-qubit state is presented. In this scheme, the quantum channel is provided by a pair of four-qubit generalized (G) Bell-states, which are decomposable. We show that not all possible distributions of entangled qubits to four communicating parties result in successful open-destination teleportation. We theoretically prove that two Bell-state measurements performed by a sender result in splitting, distributing, and locking the two-qubit state among three different receivers. The complete details of the procedure for unlocking the shared two-qubit state and eventually regenerating it at the location of any one of the three receiving stations is theoretically analyzed. This unlocking and regeneration procedure consists of local operations and classical communication (LOCC) performed by the remaining two receivers.
Full detail of a proposed experiment required for implementing and verifying a theoretical scheme for four-partite splitting and open-destination teleportation of an arbitrary two-qubit photonic state is discussed. In this proposed experiment the quantum channel is provided by a pair of decomposable generalized (G) Bell states, which offer the experimental advantage that they can be very easily generated in photonic experiments. Our experiment is based on generating a two-qubit photonic state by ultrafast spontaneous parametric downconversion in nonlinear crystal and relies on Bell-state measurements, which in this experiment are performed by an optical Bell-state analyzer that can unambiguously determine all four Bell states. In this proposed experiment unitary transformation required at the destination station is implemented using a quantum control NOT gate. We finally show that in our four-partite optical system the two-qubit photonic state originally prepared at a sending station can be experimentally split and subsequently regenerated at any one of the three distinct receiving stations.
Quantum teleportation provides a “bodiless” way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a fourqubit cluster state of the form | ϕ > 1234 = α |0000>+ β |1010>+ γ |0101>- η |1111>, as the quantum channel, where the nonzero real numbers α , β , γ , and η satisfy the relation j α j2 + | β | 2 + | γ | 2 + | η | 2 = 1. With the introduction of an auxiliary qubit with state |0>, using a suitable unitary transformation and a positive-operator valued measure (POVM), the receiver can recreate the state of the original qubit. An important advantage of the teleportation scheme demonstrated here is that, if the teleportation fails, it can be repeated without teleporting copies of the unknown quantum state, if the concerned parties share another pair of entangled qubit. We also present a protocol for quantum information splitting of an arbitrary two-particle system via the aforementioned cluster state and a Bell-state as the quantum channel. Problems related to security attacks were examined for both the cases and it was found that this protocol is secure. This protocol is highly efficient and easy to implement.
We propose two schemes for splitting single- and two-qubit states by using four-particle genuine entangled state as the quantum channel. After the sender performs Bell-basis (or three-partite GHZ- basis) measurements on her particles, and the cooperators operate single-particle measurements on their particles, the state receiver can reconstruct the original state of the sender by applying the appropriate unitary operation. In particular, in the scheme for splitting two-qubit state, the receiver needs to introduce an auxiliary particle and carries out a C-NOT operation.
Recently, there is much interest in the study of quantum teleportation. Its marvelous security property makes it particularly attractive as potential means for future communication. Uncertain principal and no-cloning theories of quantum mechanics forbid exact copy of quantum states. To solve the problem, quantum teleportation devides message state into two parts: classical message and quantum message which are transmitted through relevant classical and quantum channels from a sender Alice to a distant receiver Bob, respectively. According to both message states, Bob can recover the original message state with certain possibility. Utilizing the general quantum teleportation protocol, in this scheme, a new method is presented by which multi-qubit quantum information can be teleported in a much easier way. It has been extended to teleportation of an arbitrary N-qubit state via entanglement swapping and probabilistic teleportation is investigated as well, which has a more general meaning. N non-maximally entangled triplet GHZ states (Greenberger-Home-Zeilinger), taking the place of the previous EPR states (Einstein-Podolsky-Rosen), serve as quantum channels, which avoids introducing extra auxiliary qubit. In order to complete the teleportation, Alice has to devide all qubits into N parts and make Bell-State measurement on qubit pair (i, x(subscript i)) and tell Bob the measurement result through classical channel, then Bob perform some simple local operations on qubits (y(subscript i), z(subscript i)) to finish teleporting the i-th qubit. Conditioned on N-times similar repeat, Bob can faithfully reconstruct the initial state. Results show that, in this method, the identification difficulty of entangled states is considerably reduced, the new method is more feasible in technique. And the total possibility of successful teleportation is (The equation is abbreviated). As a special case, teleportation of an arbitrary two-qubit state is proposed.
A scheme is proposed for quantum information splitting of a two-qubit Bell state by using a four-qubit entangled state as a quantum channel. In the scenario, it is supposed that there are three legitimate parties, say Alice, Bob and Charlie. Alice is the sender of quantum information. Bob and Charlie are two agents. Alice first performs GHZ state measurement and tells Bob and Charlie the measurement results via a classical channel. It is impossible for Bob to reconstruct the original state with local operations unless help is obtained from Charlie. If Charlie allows Bob to reconstruct the original state information, he needs to perform a single-qubit measurement and tell Bob the measurement result. Using the measurement results from Alice and Charlie, Bob can reconstruct the original state. We also consider the problem of security attacks. This protocol is considered to be secure.