Entropy lower bounds of quantum decision tree complexity

Aug 22, 2000 - which the oracle and the computer exchange several rounds of messages, each round consisting of O(log ... Unlike classical decision tre...

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Sep 29, 2013 - §Research partially supported by the MTA RAMKI Lendület Cryptography Research Group, NSERC, the Hun- garian OTKA grant NN-102029 and an exchange ...... Finding the maximum, i.e., maxC ρα(C) therefore answers the question whether α

Apr 15, 2002 - quantum communication complexity and nondeterministic quantum communication complexity. We develop several other lower bound methods based on the Fourier transform, notably showing that. √¯s(f)/ log n, for the average sensitivity ¯

Sep 21, 2005 - As our measure of complexity, we use the query complexity. The query complexity of an algorithm A computing a function F is the number of queries used by A. The query complexity of. F is the minimum query complexity of any algorithm co

Nov 30, 2006 - arXiv:quant-ph/0611294v1 30 Nov 2006. Quantum Lower Bounds by Entropy Numbers. Stefan Heinrich. Department of Computer Science.

Sep 22, 2009 - For example on Z2, a bipartite graph, one can man all sites on 2Z2 ..... ible with Proposition 2.3. we will try out a symmetric variant of the theme.

Section 2 reviews standard notions and facts about Fourier transform and influence of variables. Section ... All probability distributions are uniformly random over the corresponding domain. + usually is bitwise XOR, and · is usually inner product.

Jan 16, 2014 - studied scenario goes beyond quantum processes and includes the communication complexity scenario introduced by Yao. We illustrate the method by analytically deriving some non-trivial lower bounds. Finally, we conjecture the lower boun

Moreover, in the era of big data, other general- purpose methods .... Finally, our analysis extends to bounded-error algorithms: even if the algorithm is allowed to .... inf. A∈A(O). EF [TA(F, e)] , leading to stronger lower bounds. We will also bo

May 2, 2017 - function classes and domains such as Lp-balls and the box. Most of the lower bounds were established in [7], [8], [9]. These bound worst-case complexity using the technique of resisting oracles, continuously changing the function f to p

Feb 18, 2013 - The decision tree model captures the complexity of computing functions f : Xm → Y in a setting where the quantity of interest is the number of queries to the input (see [1] for a good review of the model). We are allowed to query ind

Apr 6, 2015 - The goal is to compute f(x), while minimizing the number of queries made to the black box. For a function f : {0,1}n → {0,1}, let D(f) denote the deterministic query complexity (or decision tree complexity) of computing f, the minimum

range. As a corollary, we obtain a better lower bound on the polynomial degree of the two-level. AND–OR tree. 1 Introduction. Quantum computing provides speedups for many search problems. The most famous ... In at least two cases, the lower bounds

Jun 8, 2017 - by a contact isotopy that is everywhere positively transverse to the contact structure. In other words, ϕ ...... E-mail address: [email protected]

In the query model, the input is accessed using oracle queries, and the query complexity of an algorithm is the .... be a binary string of length log n, with K(z|A) ≥ log n. Let j be ...... nical Report quant-ph/0310107, arXiv archive, 2003. [Yao77

Apr 12, 2005 - simulation, we show that if the quantum k-party communication complexity of a func- tion f is Ω( n. 2k ), then its classical k-party communication is Ω( n. 2k/2 ). Finding such an f would allow us to prove strong classical lower boun

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Mar 18, 2013 - which is the homogeneous part of degree n of the polynomial ring C[X1,...,Xn2 ]. ... the action of Un, i.e., ∀u ∈ Un : uf = f, is called a high- est weight vector (HWV) of V ...... University of. Paderborn, 2012, Online available a

Nov 9, 2016 - is infinite, and the second is a linear lower bound on the alternating online state complexity of the prime numbers .... realtime if there exists a bound K such that its input head can stay at the same place for at most K ..... nating O

considered by Yao [33] and the first example where quantum beats classical communication complexity was given in .... entanglement, C∗(f) denotes the cost of a protocol that communicates classical bits but can make use of ..... Corollary 7 If g is

Apr 6, 2008 - The gravitational entropy of the Universe is large and subtle to calculate. A lower bound is well known ... As interest grows in pursuing alternatives to the Big Bang, including cyclic cosmologies, it becomes more pertinent ... intuitiv

Jun 16, 2016 - lemma, which is a variant of Strassen's [Str73] homogenization technique for efficiently computing the low-degree homogeneous components of an unbounded degree circuit. As weaker models of computation (such as formulas and branching pr

Jul 17, 2018 - and de Wolf provides more examples of this proof technique [DW11]. ... Høyer, Mosca and de Wolf [HMdW03]. Ω(. √ n) ...... Ryan O'Donnell.

May 26, 2017 - College of Science, University of Tehran, Tehran, Iran. Abstract. We study the relations between the ...... i(n) < 2−n(s(ω)−2ǫ)} . (6.12). Using (5.9), the cardinality of the complement (B. (n) ǫ. )c of the latter subset is boun