Related papers: The quantum query complexity of composition with a…
Consistent query answering is the problem of computing the answers from a database that are consistent with respect to certain integrity constraints that the database as a whole may fail to satisfy. Those answers are characterized as those…
The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system…
We use the venerable "fooling set" method to prove new lower bounds on the quantum communication complexity of various functions. Let f:X x Y-->{0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its…
We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
The main principle of affine quantum gravity is the strict positivity of the matrix \{\hat g_{ab}(x)\} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle,…
A crucial goal of quantum information is to find new ways to exploit the properties of quantum devices as resources. One of the prominent properties of quantum devices of particular interest is their negativity in quasi-probability…
We show that for a relation $f\subseteq \{0,1\}^n\times \mathcal{O}$ and a function $g:\{0,1\}^{m}\times \{0,1\}^{m} \rightarrow \{0,1\}$ (with $m= O(\log n)$), $$\mathrm{R}_{1/3}(f\circ g^n) = \Omega\left(\mathrm{R}_{1/3}(f) \cdot…
We propose a new definition of quantum Las Vegas query complexity. We show that it is exactly equal to the quantum adversary bound. This is achieved by a new and very simple way of transforming a feasible solution to the adversary…
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization…
Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits…
Probably the simplest and most frequently used way to illustrate the power of quantum computing is to solve the so-called {\it Deutsch's problem}. Consider a Boolean function $f: \{0,1\} \to \{0,1\}$ and suppose that we have a (classical)…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevance. We present two protocols for a classical verifier to verifiably delegate a quantum computation to two…
We consider the problem of zero-error function computation with side information. Alice and Bob have correlated sources $X,Y$ with joint p.m.f. $p_{XY}(\cdot, \cdot)$. Bob wants to calculate $f(X,Y)$ with zero error. Alice encodes…
We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…
Security of quantum key distribution (QKD) relies on certifying that observed correlations arise from genuine quantum entanglement rather than eavesdropper manipulation. Theoretical security proofs assume idealized conditions, practical…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently,…