The Power of Unentanglement
arXiv:0804.0802
Abstract
The class QMA(k), introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give any evidence that k quantum proofs are more powerful than one? Does QMA(k)=QMA(2) for k>=2? Can QMA(k) protocols be amplified to exponentially small error? In this paper, we make progress on all of the above questions. First, we give a protocol by which a verifier can be convinced that a 3SAT formula of size n is satisfiable, with constant soundness, given ~O(sqrt(n)) unentangled quantum witnesses with O(log n) qubits each. Our protocol relies on the existence of very short PCPs. Second, we show that assuming a weak version of the Additivity Conjecture from quantum information theory, any QMA(2) protocol can be amplified to exponentially small error, and QMA(k)=QMA(2) for all k>=2. Third, we prove the nonexistence of "perfect disentanglers" for simulating multiple Merlins with one.
Several errors fixed; based amplification result on "Weak Additivity Conjecture" rather than now-falsified Additivity Conjecture; added some new observations due to F. Brandao. To appear in Theory of Computing
References in corpus (9)
- Mixed State Entanglement and Quantum Error Correction
- Strengths and Weaknesses of Quantum Computing
- Superadditivity of communication capacity using entangled inputs
- "Squashed Entanglement" - An Additive Entanglement Measure
- N-representability is QMA-complete
- Quantum Randomness and Nondeterminism
- Interaction in Quantum Communication
- QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum Protocols
- A quantum characterization of NP