Related papers: Variations on Classical and Quantum Extractors
We study the point spectrum of a periodic quantum tree equipped with a Schr\"odinger type differential operator with delta-type vertex conditions, using subsets of the compact graph that generates the tree. We prove analogs of existing…
It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability…
It is well known that many operations in quantum information processing depend largely on a special kind of quantum correlation, that is, entanglement. However, there are also quantum tasks that display the quantum advantage without…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
In privacy amplification, two mutually trusted parties aim to amplify the secrecy of an initial shared secret $X$ in order to establish a shared private key $K$ by exchanging messages over an insecure communication channel. If the channel…
Device-independent (DI) quantum cryptography aims at providing secure cryptography with minimal trust in, or characterisation of, the underlying quantum devices. A key step in DI protocols is randomness extraction (or privacy…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
This note introduces "Q-marginals", which are quantum states encoding some probability distribution in a manner suitable for use in Quantum Monte Carlo Integration (QMCI), and shows that these can be prepared directly from a classical…
A *dimension extractor* is an algorithm designed to increase the effective dimension -- i.e., the amount of computational randomness -- of an infinite binary sequence, in order to turn a "partially random" sequence into a "more random"…
The small angle scattering (by a gravitational field) of classical and quantum particles is considered and compared. It is suggested that the differences in small angle scattering of particles with spin 0, 1, 2 are due to the nonzero…
We introduce different ensembles of random Lindblad operators $\cal L$, which satisfy quantum detailed balance condition with respect to the given stationary state $\sigma$ of size $N$, and investigate their spectral properties. Such…
Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…
Measurements on entangled quantum systems necessarily yield outcomes that are intrinsically unpredictable if they violate a Bell inequality. This property can be used to generate certified randomness in a device-independent way, i.e.,…
We show that in device independent quantum key distribution protocols the privacy of randomness is of crucial importance. For sublinear test sample sizes even the slightest guessing probability by an eavesdropper will completely compromise…
The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow "far" from having that property, a tester should…
The simulation of the spectra measured in nuclear magnetic resonance (NMR) spectroscopy experiments is a computationally non-trivial problem which, due to its natural interpretation as a quantum spin problem, maps in a straightforward way…
The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
Random circuit sampling has become a popular means for demonstrating the superiority of quantum computers over classical supercomputers. While quantum chips are evolving rapidly, classical sampling algorithms are also getting better and…
Experimental demonstration of the quantum advantage over classical simulations with Boson Sampling is currently under intensive investigation. There seems to be a scalability issue to the necessary number of bosons on the linear optical…