منابع مشابه
On perfect completeness for QMA
Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with onesided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a “quantum oracle” relative to which QMA 6= QMA1. As a byproduct, we find that there are facts about quantum complexity classes that are classically relativizing but not ...
متن کاملTowards Perfect Completeness in QMA
This talk presents two results, both of which are quantumly nonrelativizing, and arguably step towards affirmatively settling the QMA versus QMA1 problem (i.e., the problem of whether quantum Merlin-Arthur proof systems with one-sided bounded error of perfect completeness have verification power equivalent to general quantum Merlin-Arthur proof systems with two-sided bounded error). First, it i...
متن کاملA Hypergraph Dictatorship Test with Perfect Completeness
A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan in [21] and serves as a key component in their unique games based PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are o(1). The test in [21] makes q ≥ 3 queries and has amortized query...
متن کاملAn Improved Dictatorship Test with Perfect Completeness
A Boolean function f : {0, 1} → {0, 1} is called a dictator if it depends on exactly one variable i.e f(x1, x2, . . . , xn) = xi for some i ∈ [n]. In this work, we study a k-query dictatorship test. Dictatorship tests are central in proving many hardness results for constraint satisfaction problems. The dictatorship test is said to have perfect completeness if it accepts any dictator function. ...
متن کاملQuery Efficient PCPs with Perfect Completeness
For every integer k > 0, and an arbitrarily small constant ε > 0, we present a PCP characterization of NP where the verifier uses logarithmic randomness, non-adaptively queries 4k + k2 bits in the proof, accepts a correct proof with probability 1, i. e., it has perfect completeness, and accepts any supposed proof of a false statement with probability at most 2−k 2 + ε . In particular, the verif...
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ژورنال
عنوان ژورنال: Quantum Information and Computation
سال: 2009
ISSN: 1533-7146,1533-7146
DOI: 10.26421/qic9.1-2-5