Related papers: Origin of the quantum speed-up
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
On the basis of introspective analysis, we establish a crucial requirement for the physical computation basis of consciousness: it should allow processing a significant amount of information together at the same time. Classical computation…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…
We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only sequential measurements are allowed. Sequential measurements from…
We prove the following conjecture, raised by Aaronson and Ambainis in 2008: Let $f:\{-1,1\}^n \rightarrow [-1,1]$ be a multilinear polynomial of degree $d$. Then there exists a variable $x_i$ whose influence on $f$ is at least…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Quantum steering is a relatively simple test for quantumness of correlations, proving that the values of quantum-mechanical measurement outcomes come into being only in the act of measurement. By exploiting quantum correlations Alice can…
We study prepare-and-measure experiments where the sender (Alice) receives trusted quantum inputs but has an untrusted state-preparation device and the receiver (Bob) has a fully-untrusted measurement device. A distributed-sampling task…
One-sided output secure function evaluation is a cryptographic primitive where the two mutually distrustful players, Alice and Bob, both have a private input to a bivariate function. Bob obtains the value of the function for the given…
Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics. It is based on the assumption that Alice and Bob can choose measurements from a measurement set containing…
Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…
Lying at the heart of quantum mechanics, coherence has recently been studied as a key resource in quantum information theory. Quantum steering, a fundamental notion originally considered by Schr{\"o}dinger, has also recently received much…
We compare quantum and classical machines designed for learning an N-bit Boolean function in order to address how a quantum system improves the machine learning behavior. The machines of the two types consist of the same number of…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two partite system, Alice and Bob each…
The characterization of quantum processes is a key tool in quantum information processing tasks for several reasons: on one hand, it allows to acknowledge errors in the implementations of quantum algorithms; on the other, it allows to…
Alice, who does not have any sophisticated quantum technology, delegates her quantum computing to Bob, who has a fully-fledged quantum computer. Can she check whether the computation Bob performs for her is correct? She cannot recalculate…
We investigate the feasibility of quantum seals. A quantum seal is a state provided by Alice to Bob along with information which Bob can use to make a measurement, "break the seal," and read the classical message stored inside. There are…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…