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Bidirectional Teleportation of a Pure EPR State by using GHZ states
Shima Hassanpour, Monireh Houshmand
TL;DR
Earlier bidirectional protocols were described as exchanging single-qubit states, while this paper proposes simultaneous exchange of pure EPR states. It uses entanglement swapping to share two GHZ states as a channel, and reports that each user can reconstruct the other's state after measurements and suitable unitary operations.
Problem
Method
Results
Takeaways & Limitations
The authors describe the protocol as economical because it transmits two-qubit EPR states where previous schemes exchanged single-qubit states using four-qubit channels.
Source: §5 · p. 5
Abstract
from arXiv · showhide
In the present paper, a novel bidirectional quantum teleportation protocol is proposed. By using entanglement swapping technique, two GHZ states are shared as a quantum channel between Alice and Bob as legitimate users. In this scheme, based on control-not operation, single-qubit measurement and appropriate unitary operations, two users can simultaneously transmit a pure EPR state to each other. While, in the previous protocols, the users can just teleport a single-qubit state to each other via more than four-qubit state. Therefore, the proposed scheme is economical compared with previous protocols.
1 Introduction
Earlier bidirectional teleportation protocols enabled exchange of single-qubit states, while this paper proposes simultaneous exchange of pure EPR states using two GHZ states. The protocol uses controlled-not operations, single-qubit measurements, and suitable unitary operations.
1 Introduction
- Earlier work included bidirectional controlled-teleportation schemes using five- and six-qubit entangled channels, as well as bidirectional teleportation with a four-qubit cluster channel.The paper also reports that Shukla et al. [17] argued Li et al.'s scheme [10] was not a BQCT protocol.Source: §1 · p. 1
- Earlier bidirectional schemes allowed users to teleport single-qubit states, whereas this protocol targets simultaneous exchange of pure EPR states.The paper identifies four-qubit channels as the best case among previous protocols [9 −16].Source: §1 · p. 1
- The proposed scheme uses two GHZ states as a channel and combines controlled-not operations, single-qubit measurements, and suitable unitary operations.Source: §1 · p. 1
2 Six-qubit entangled GHZ state as a quantum channel
The paper describes entanglement swapping between two three-particle GHZ states as a route to a six-qubit entangled quantum channel. Alice's GHZ-basis measurement leaves corresponding GHZ-state pairs with equal probabilities.
2 Six-qubit entangled GHZ state as a quantum channel
- The entanglement-swapping discussion starts from two GHZ states and uses the resulting six-qubit entangled state as the teleportation channel.The text says similar results can be obtained if Alice and Bob share other GHZ states.Source: §2 · p. 2
- The passage presents the GHZ states used in the swapping construction as superpositions of basis states.Source: §2 · p. 2
- A GHZ-basis measurement by Alice on her three qubits yields four corresponding GHZ-state pairs, each with probability 1/4.The two initially shared states are three-particle GHZ states, with qubits 1, 3, and 5 held by Alice and 2, 4, and 6 by Bob.Source: §2 · p. 2
3 Description of the Proposed protocol
Alice and Bob each begin with a pure two-qubit entangled state and share a two-GHZ channel. They use local controlled-not operations and single-qubit measurements, announce results, and apply suitable unitaries to reconstruct each other's states.
3 Description of the Proposed protocol
- Alice and Bob's inputs are pure two-qubit entangled states, and the shared channel consists of two GHZ states distributed across their qubits.The input amplitudes are normalized separately for Alice and Bob.Source: §3 · p. 2
- Each user applies a controlled-not operation from an input qubit to a channel qubit, then performs Z-basis and X-basis single-qubit measurements on designated qubits.Alice uses A1 as control and a1 as target; Bob uses B1 as control and b3 as target.Source: §3 · pp. 2–3
- The initial measurement outcomes can leave the remaining particles in any of 16 possible collapsed states, all with equal probability.Table I is captioned as relating users' measurement results to the corresponding collapsed state.Source: §3 · p. 3, Table I · p. 3
- After sharing their results, Alice and Bob perform further X-basis measurements and announce those results before applying the corresponding reconstruction operations.The supplied procedure specifies measurements on A1 and B1; the text states that withholding a user's results prevents the other from reconstructing the state.Source: §3 · p. 3
- After the users' measurements and suitable unitary operations, each reconstructs the other's two-qubit entangled state, completing bidirectional teleportation.Table II relates measurement results to the corresponding unitary operations.Source: §3 · p. 4, Table II · p. 4
4 Comparison
The comparison emphasizes that the protocol exchanges pure EPR states simultaneously using two GHZ states, whereas previous schemes were limited to single-qubit exchange. It also contrasts the single-qubit measurements and GHZ-based channel with earlier measurement and channel choices.
4 Comparison
- The protocol simultaneously teleports a pure EPR pair in each direction using two GHZ states, while previous schemes' best case exchanged single-qubit states through a four-qubit channel.The paper says those earlier protocols would need to be run twice to teleport a two-qubit state.Source: §4 · p. 4
- Unlike earlier works using two-qubit measurements, the proposed protocol uses single-qubit measurements, which the authors describe as more efficient.The efficiency comparison is attributed to [20].Source: §4 · p. 4
- Entanglement swapping is presented as a way to share the two-GHZ channel, which the authors say is easier to prepare experimentally than cluster or brown-state channels.The scheme requires preserving entanglement among three qubits, which the authors contrast with the greater complication of preserving it among more than three.Source: §4 · p. 4
5 Conclusions
The paper concludes with a bidirectional teleportation protocol that uses two GHZ states to exchange pure EPR states simultaneously. It compares the protocol with prior single-qubit schemes and identifies controlled teleportation and larger states as future extensions.
5 Conclusions
- Two GHZ states serve as an entanglement-swapping channel for Alice and Bob to simultaneously teleport pure EPR states using single-qubit measurements, controlled-NOT operations, and suitable unitaries.If either user does not cooperate, the receiver cannot reconstruct the original state.Source: §5 · p. 5
- Unlike prior schemes that teleport single-qubit states, the proposed protocol exchanges two-qubit pure EPR states and is described as economical compared with other schemes.The conclusion contrasts this with prior single-qubit teleportation using four-qubit channels in the best case.Source: §5 · p. 5
- Extending the protocol to controlled teleportation under Charlie’s control, with Alice and Bob teleporting more than two qubits, is proposed as future work.The authors express this as a hoped-for extension.Source: §5 · p. 5