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arXiv:0812.4214 · Journal of Physics B Atomic Molecular and Optical Physics

Minimal classical communication and measurement complexity for quantum information splitting

Zhan-jun Zhang, Chi-Yee Cheung

Published Dec 20, 2007• 65 citations
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Abstract

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.

DOI
10.1088/0953-4075/41/1/015503

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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 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.
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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.