Related papers: Experimental Tests of Classical and Quantum Dimens…
A test of quantumness is a protocol where a classical user issues challenges to a quantum device to determine if it exhibits non-classical behavior, under certain cryptographic assumptions. Recent attempts to implement such tests on current…
It is shown that a good estimate of the fidelity of an experimentally realized quantum process can be obtained by measuring the outputs for only two complementary sets of input states. The number of measurements required to test a quantum…
This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…
Quantum digital signatures (QDS) provide a means for signing electronic communications with informationtheoretic security. However, all previous demonstrations of quantum digital signatures assume trusted measurement devices. This renders…
Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as…
The development of small-scale digital and analog quantum devices raises the question of how to fairly assess and compare the computational power of classical and quantum devices, and of how to detect quantum speedup. Here we show how to…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
We introduce a model of classical and quantum observation based on contextuality and dynamically evolving apparatus. Power sets of classical bits model the four classical states of elementary detectors, viz. the two normal yes/no signal…
In a recent paper, a "distance" function, \cal D, was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a "distance", D, which measures the distance between either…
A dimension witness is a criterion that sets a lower bound on the dimension needed to reproduce the observed data. Three types of dimension witnesses can be found in the literature: device-dependent ones, in which the bound is obtained…
A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al.,…
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new…
A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify the quantum advantage of an untrusted prover. That is, a quantum prover can correctly answer the verifier's challenges and…
We introduce the notion of compatibility dimension for a set of quantum measurements: it is the largest dimension of a Hilbert space on which the given measurements are compatible. In the Schr\"odinger picture, this notion corresponds to…
We compare the power of quantum and classical physics in terms of randomness certification from devices which are only partially characterised. We study randomness certification based on state discrimination and take noncontextuality as the…
Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability…
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in…