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arXiv:0907.3532

In how many ways can quantum information be split ?

Sreraman Muralidharan, Siddharth Karumanchi, Srinatha Narayanaswamy, R. Srikanth, Prasanta Kumar Panigrahi

Published Jul 21, 2009• 4 citations
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Abstract

We establish a theoretical understanding of the entanglement properties of a physical system that mediates a quantum information splitting protocol. We quantify the different ways in which an arbitrary $n$ qubit state can be split among a set of $k$ participants using a $N$ qubit entangled channel, such that the original information can be completely reconstructed only if all the participants cooperate. Based on this quantification, we show how to design a quantum protocol with minimal resources and define the splitting efficiency of a quantum channel which provides a way of characterizing entangled states based on their usefulness for such quantum networking protocols.

DOI
10.48550/arxiv.0907.3532

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We establish a theoretical understanding of the entanglement properties of a physical system that mediates a quantum information splitting protocol. We quantify the different ways in which an arbitrary nnn qubit state can be split among a set of kkk participants using a NNN qubit entangled channel, such that the original information can be completely reconstructed only if all the participants cooperate. Based on this quantification, we show how to design a quantum protocol with minimal resources and define the splitting efficiency of a quantum channel which provides a way of characterizing entangled states based on their usefulness for such quantum networking protocols.
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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.
A scheme is presented for quantum information splitting of an unknown two-particle entangled state by using five-particle cluster state as the quantum channel.The sender(Alice),the receiver(Bob) and the controller(Charlie) share the quantum channel.The sender Alice sends the quantum information to the receiver Bob,anyone can not obtain the quantum information,unless they cooperate with each other.The receiver can reconstruct two-particle entangled state by performing appropriate unitary transformations on his qubits after the sender and controller perform the appropriate measurements on their qubits.respectively.
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.
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.