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Chinese Journal of Quantum Electronics

Minimal measurement complexity for quantum information splitting of two-qubit state

Guixia Pan

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

A quantum information splitting scheme of two-qubit state is proposed by using two asymmetric W states as quantum channel.It's showed that if the two-qubit state is known to the sender(Alice),then she can split quantum information and distribute it to the receivers(Bob and Charlie) by performing a two-qubit projective measurement.Bob and Charlie first perform a collective unitary operation on their qubits,and then Charlie can recover the initial quantum state by implementing two single-qubit unitary operations.So the scheme reduces greatly the measurement complexity.The success probability and classical communication cost are calculated within the scheme.

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A quantum information splitting scheme of two-qubit state is proposed by using two asymmetric W states as quantum channel.It's showed that if the two-qubit state is known to the sender(Alice),then she can split quantum information and distribute it to the receivers(Bob and Charlie) by performing a two-qubit projective measurement.Bob and Charlie first perform a collective unitary operation on their qubits,and then Charlie can recover the initial quantum state by implementing two single-qubit unitary operations.So the scheme reduces greatly the measurement complexity.The success probability and classical communication cost are calculated within the scheme.
We propose a scheme for splitting a two-qubit quantum information by using two asymmetric W states as quantum channel. In this scheme the split state is assumed to be completely known by the sender. Because of this, during the splitting process, the sender only needs to perform a two-qubit projective measurement. Once the sender announces the measurement result in terms of the prior agreement, then using this message the two receivers can recover the quantum information via their mutual assistance. We calculate the success probability and classical communication cost of the scheme. In general, the splitting success probability (SSP) is 1/4 and the average classical communication cost is 0.25 bit. However, we find that for some states the SSP can reach 0.5 or even unity after consuming a little additional classical resource.
We present two quantum information splitting schemes using respectively tripartite GHZ and asymmetric W states as quantum channels. We show that if the secret state is chosen from a special ensemble and known to the sender (Alice), then she can split and distribute it to the receivers Bob and Charlie by performing only a single-qubit measurement and broadcasting a one-cbit message. It is clear that no other schemes could possibly achieve the same goal with simpler measurement and less classical communication. In comparison, existing schemes work for arbitrary quantum states which need not be known to Alice; however she is required to perform a two-qubit Bell measurement and communicate a two-cbit message. Hence there is a trade-off between flexibility and measurement complexity plus classical resource. In situations where our schemes are applicable, they will greatly reduce the measurement complexity and at the same time cut the communication overhead by one half.
We present a quantum information splitting scheme of a two-qubit state by using two Greenberger–Horne–Zeilinger (GHZ) states as quantum channels. In this scheme, since the sender Alice knows the quantum information in priori, she only needs to perform a two-qubit measurement and publish two classical bits for her two agents Bob and Charlie to reconstruct the quantum information via their mutual assistance. We calculate the success probability and classical communication cost within the scheme. In the general case, Alice can successfully split the state with probability 25% (probabilistic) and the classical communication cost is 4 classical bits. However, in some special cases, the secret states are chosen from a special ensemble, the success probability of our scheme can be increased to 50% or even to 100% (deterministic) after consuming some extra classical bits.
Through introducing the new application of a genuinely entangled six-qubit state,quantum information splitting of an arbitrary two-qubit state was investigated.For the quantum information splitting,a genuinely entangled six-qubit state was shared by a sender(Alice),a controller(Charlie) and a receiver(Bob).The sender firstly performed twice Bell-state measurements,and then the controller made a Bell-state measurement.Finally the receiver can reconstruct the arbitrary two-qubit state by performing some appropriate unitary transformations on his qubits after he knew the measured results of both the sender and the controller.This quantum information splitting scheme is deterministic,i.e.the probability of success is 100%.In comparison with the quantum information splitting scheme using the same quantum channel the sender and the controller only need to perform Bell-state measurements,not joint multi-qubit measurement,which makes this scheme simpler and easier,and can be fulfilled based on present experimental technology.
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 scheme is presented for splitting three-particle GHZ-class states by using two GHZ states as the quantum channel.We show that if the sender Alice knows the initial state in prior,she only needs to implement a two-qubit projective measurement for her two receivers Bob and Charlie to recover the original state via their mutual assistance.In the scheme,the success probability and classical communication cost is calculated.In general case,Alice can successfully split the state with probability 1/4 and the classical communication cost is 3/4 classical bit.However,in situations of five special states,the success probability of our scheme can be increased to 1/2 or even to 1 after consuming some extra classical bits.