Related papers: Entropy lower bounds of quantum decision tree comp…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
In this paper, we introduce the hybrid query complexity, denoted as $\mathrm{Q}(f;q)$, which is the minimal query number needed to compute $f$, when a classical decision tree is allowed to call $q'$-query quantum subroutines for any $q'\leq…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
We present a near-optimal quantum algorithm, up to logarithmic factors, for estimating the Shannon entropy in the quantum probability oracle model. Our approach combines the singular value separation algorithm with quantum amplitude…
We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that $D(f) = O(Q_1(f)^3)$…
For any function $f: X \times Y \to Z$, we prove that $Q^{*\text{cc}}(f) \cdot Q^{\text{OIP}}(f) \cdot (\log Q^{\text{OIP}}(f) + \log |Z|) \geq \Omega(\log |X|)$. Here, $Q^{*\text{cc}}(f)$ denotes the bounded-error communication complexity…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…
The degree of a polynomial representing (or approximating) a function f is a lower bound for the number of quantum queries needed to compute f. This observation has been a source of many lower bounds on quantum algorithms. It has been an…
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…
The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPR-pairs). Some lower bound techniques are available for qubit communication…
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…
We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…
Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower…