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

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

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 ¯

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

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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

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

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

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

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

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]

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

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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.