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International Journal of Quantum Information

PERFECT TELEPORTATION, SUPERDENSE CODING VIA A KIND OF W-CLASS STATE

Liying Shangguan, Hong-xiang Sun, Xiu‐Bo Chen, Heng-Yue Jia, Qiaoyan Wen, Fu-Chen Zhu

Published Dec 1, 2010• 6 citations
Publisher

Abstract

Perfect teleportation and superdense coding are discussed via a special kind of W-state. It is shown that the state can be used for perfect teleportation of the state x|0〉⊗N + y|1〉⊗N. And the state can be utilized for superdense coding. Moreover, it is demonstrated that the sender can transmit N classical bits to the receiver by sending N − 1 qubits.

DOI
10.1142/s0219749910006964

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Perfect teleportation and superdense coding are discussed via a special kind of W-state. It is shown that the state can be used for perfect teleportation of the state x|0〉⊗N + y|1〉⊗N. And the state can be utilized for superdense coding. Moreover, it is demonstrated that the sender can transmit N classical bits to the receiver by sending N − 1 qubits.
As we know, the states of triqubit systems have two important classes: GHZ-class and W-class. In this paper, the states of W-class are considered for teleportation and superdense coding, and are generalized to multi-particle systems. First we describe two transformations of the shared resources for teleportation and superdense coding, which allow many new protocols from some known ones for that. As an application of these transformations, we obtain a sufficient and necessary condition for a state of W-class being suitable for perfect teleportation and superdense coding. As another application, we find that state ∣W>123=1/2(∣100>123+∣010>123+sqrt2∣001>123)|W>_{123}={1/2}(|100>_{123}+|010>_{123}+\\sqrt{2}|001>_{123})∣W>123​=1/2(∣100>123​+∣010>123​+sqrt2∣001>123​) can be used to transmit three classical bits by sending two qubits, which was considered to be impossible by P. Agrawal and A. Pati [Phys. Rev. A to be published]. We generalize the states of W-class to multi-qubit systems and multi-particle systems with higher dimension. We propose two protocols for teleportation and superdense coding by using W-states of multi-qubit systems that generalize the protocols by using ∣W>123|W>_{123}∣W>123​ proposed by P. Agrawal and A. Pati. We obtain an optimal way to partition some W-states of multi-qubit systems into two subsystems, such that the entanglement between them achieves maximum value.
As we know, the states of triqubit systems have two important classes: GHZ-class and W-class. In this paper, the states of W-class are considered for teleportation and superdense coding, and they are generalized to multi-particle systems. First we describe two transformations on the shared resources for teleportation and superdense coding. With these transformations, we obtain a sufficient and necessary condition for a state of W-class being suitable for perfect teleportation and superdense coding. For the state which was thought to be not suitable for sending three classical bits by sending two qubits by Agrawal and Pati (2006 Phys. Rev. A 74 062320), we show that it may be used to fulfil that task, if entangled unitary operations on two qubits are allowed. We generalize the states of W-class to multi-qubit systems and multi-particle systems with higher dimension. We propose two protocols for teleportation and superdense coding by using W-states of multi-qubit systems that generalize the protocols by using | W ⟩ 123 proposed by Agrawal and Pati. We obtain an optimal way to partition some W-states of multi-qubit systems into two subsystems, such that the entanglement between them achieves maximum value.
We investigate the usefulness of a recently introduced five-qubit state by Brown et al. [I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, J. Phys. A 38, 1119 (2005)] for quantum teleportation, quantum-state sharing, and superdense coding. It is shown that this state can be utilized for perfect teleportation of arbitrary single and two-qubit systems. We devise various schemes for quantum-state sharing of an arbitrary single- and two-particle state via cooperative teleportation. We later show that this state can be used for superdense coding as well. It is found that five classical bits can be sent by sending only three quantum bits.
The paper investigates an odd particle composite quantum state combined with W-state and Bell-state.It is shown that this composite quantum state can be used to prefect teleportation of arbitrary single and two qubit,and also can be commendably utilized for superdense coding and quantum state sharing.The paper presents the measurement basis of sender and unity operations of receiver for teleportation protocol.It is found that five classical bits can be sent by conveying only three quantum bits for superdense coding.
True tripartite entanglement of the state of a system of three qubits can be classified on the basis of stochastic local operations and classical communications. Such states can be classified into two categories: GHZ states and WWW states. It is known that GHZ states can be used for teleportation and superdense coding, but the prototype WWW state cannot be. However, we show that there is a class of WWW states that can be used for perfect teleportation and superdense coding.
It is known that two local unitaries (LU) equivalent states possess the same amount of entanglement and can be used to perform the same tasks in quantum information theory (QIT). For a protocol for a task in QIT, we call a protocol LU invariant if two LU-equivalent states are either both suitable for the protocol or neither is. So far, no one has discussed whether a protocol for a task in QIT is LU invariant. In [Phys. Rev. A, 74, 062320 (2006)], Agrawal and Pati proposed the perfect teleportation protocol (PTP) and the protocol for superdense coding to transmit 2-bit classical information by sending one qubit (PSDC-2) and 3-bit classical information by sending two qubits (PSDC-3). In this paper, we show that PTP and PSDC-2 are LU invariant. That is, two LU equivalent states are suitable for PTP and PSDC-2 or neither of them is. We show that PSDC-3 is not LU invariant. We also indicate that the teleportation proposed in <cite>Nielsen</cite> is not LU invariant. We give a necessary and sufficient condition for a state to be suitable for PTP, PSDC-2, and PSDC-3, respectively. Via the LU invariance of PTP and PSDC-2, we prove that a state is suitable for PTP and PSDC-2 if and only if it has 1 ebit of shared entanglement, respectively and find all genuine entangled states and separable states which are suitable for PTP and PSDC-2, respectively. So far, no one has indicated that PTP and PSDC-2 do not require genuine entanglement. Agrawal and Pati suggested to study if there are subclasses of W SLOCC class which are suitable for PSDC-3. So far, it still remains an unsolved question. We show that any state of the SLOCC class W is not suitable for PSDC-3.