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Chinese Journal of Quantum Electronics

Quantum information splitting of product state of single-qubit state via GHZ states

LI Man-lan, Ye Liu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

A scheme is proposed for quantum information splitting(QIS) of a product state of an arbitrary single-qubit state with three-qubit GHZ states.The scheme focuses on a product state of an arbitrary single-qubit state,and the original state can be reconstructed only if the receivers cooperate with each other.Every receiver has the same authority for getting the sender's secret,and the receivers have the same probability to get the original secret,the probability to gain |φ〉_a is obtained as 2|β_b|~2,the probability to gain |φ〉_b is obtained as 2|β_a|~2.

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A scheme is proposed for quantum information splitting(QIS) of a product state of an arbitrary single-qubit state with three-qubit GHZ states.The scheme focuses on a product state of an arbitrary single-qubit state,and the original state can be reconstructed only if the receivers cooperate with each other.Every receiver has the same authority for getting the sender's secret,and the receivers have the same probability to get the original secret,the probability to gain |φ〉_a is obtained as 2|β_b|~2,the probability to gain |φ〉_b is obtained as 2|β_a|~2.
Quantum Information Splitting is an important technique used in Quantum Communication. A sender sends a quantum information (state) to several recipients during this procedure. Only all of the receivers can collectively work out to recover the content using this process. A new application of the three qubit GHZ like state is investigated for quantum information splitting (QIS) of an arbitrary two qubit state. In this paper, we have shown two three qubit GHZ like states can be used to realize the deterministic QIS of an arbitrary two qubit state by performing only the Bell state measurements. GHZ like states can easily be created. We have also shown that our scheme is secured under certain eavesdropping attacks.
Quantum information splitting(QIS) or quantum state sharing is the generalization of classical secret sharing schemes to the quantum scenario.In QIS,a piece of quantum information(in the form of a quantum state) is divided and distributed to a number of receivers.A scheme of splitting two-qubit states was proposed by using six-particle maximally entangled state as the quantum channel.Alice first performs two Bell-basis measurement and announces her measurement outcome and assigns Charlie(Bob) to reconstruct the original unknown state.If the controllers Bob(Charlie) agree to help Charlie(Bob) obtain the original state,they should perform single-particle measurements on their respective qubits.After the sender performs Bell-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.
A new application of cluster states is investigated for quantum information splitting (QIS) of an arbitrary three-qubit state. In our scheme, a four-qubit cluster state and a Bell state are shared by a sender (Alice), a controller (Charlie), and a receiver (Bob). Both the sender and controller only need to perform Bell-state measurements (BSMs), the receiver can reconstruct the arbitrary three-qubit state by performing some appropriately unitary transformations on his qubits after he knows the measured results of both the sender and the controller. This QIS scheme is deterministic.
A scheme is presented for quantum information splitting of arbitrary two-particle state by using two GHZ states as quantum channel.In this scheme,Alice performs two Bell-state measurements and publishes four classical bits to her two receivers(Bob and Charlie).If the two recipients collaborate together,they can deterministically reconstruct the quantum information by performing single-qubit measurements and two single-qubit unitary operations.And the unitary operation is explicitly given with the splitting scheme.
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.