We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits to each prover, who replies with a constant number of qubits, and (iii) completeness and soundness are separated by an inverse polynomial in $n$. As the same class of proof systems, without entanglement between the provers, is included in QCMA, our result provides the first indication that quantum multiprover interactive proof systems with entangled provers may be strictly more powerful than unentangled-prover interactive proof systems. A distinguishing feature of our protocol is that the completeness property requires honest provers to share a large entangled state, obtained as the encoding of the ground state of the local Hamiltonian via an error-correcting code. Our result can be interpreted as a first step towards a multiprover variant of the quantum PCP conjecture.
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机译：我们为n个量子位上的局部哈密顿量问题提供了一个量子交互式证明系统，其中（i）验证者与5个纠缠证明者进行了单轮交互，（ii）验证者在O（log n）位上发送经典消息到每个证明者，他们使用恒定数量的qubit进行答复，并且（iii）完整性和完整性由$ n $中的逆多项式分隔。由于QCMA中包括了没有证明者之间纠缠的同一类证明系统，因此我们的结果提供了第一个迹象，即证明有纠缠证明者的量子多证明人交互式证明系统可能比无证明提供者交互式证明系统更强大。我们协议的一个显着特征是，完整性属性需要诚实的证明来共享大的纠缠态，这是通过纠错码对本地哈密顿量的基态进行编码而获得的。我们的结果可以解释为迈向量子PCP猜想的多重证明者的第一步。
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