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In this letter a new gauge invariant, metric independent action is introduced from which Witten's Topological Quantum Field Theory may be obtained after gauge fixing using standard BRST techniques. In our model the BRST algebra of…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
We show the relationship between the Fourier coefficients and the barren plateau problem emerging in parameterized quantum circuits. In particular, the sum of squares of the Fourier coefficients is exponentially restricted concerning the…
Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an…
We present the first experimental confirmation of the quantum-mechanical prediction of stronger-than-binary correlations. These are correlations that cannot be explained under the assumption that the occurrence of a particular outcome of an…
Application of the uncertainty principle to conditional measurements is investigated, and found to be valid for measurements on separated sub-systems. In light of this, an apparent violation of the uncertainty principle obtained by Kim and…
Wigner's thought experiment illustrates quantum theory's measurement problem by considering an observer who measures a quantum system inside a sealed lab, modeled unitarily by an outsider. Recent extensions of this thought experiment,…
We analyze anomalies in data to test the violation of Bell's inequality for the EPR-Bohm experiment. We found that the experimental correlations for photon polarization have an intriguing property. In the experimental data there are visible…
The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by such physicists as J. S. Bell and D. Bohm. The possibility of the…
Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. Commonly, in Device-Independent and Semi-Device-Independent scenarios, randomness is certified using projective…
A disagreement of the empirical results with quantum mechanical predictions is pointed out in the experiment by M. Giustina et al. [arXiv:1212.0533].
Bohr's complementarity principle has long been a fundamental concept in quantum mechanics, positing that, within a given experimental setup, a quantum system (or quanton) can exhibit either its wave-like character, denoted as $W$, or its…
Buhrman, Patro, and Speelman presented a framework of conjectures that together form a quantum analogue of the strong exponential-time hypothesis and its variants. They called it the QSETH framework. In this paper, using a notion of quantum…
Nowadays, it is commonly admitted that the experimental violation of Bell's inequalities that was successfully demonstrated in the last decades by many experimenters, are indeed the ultimate proof of quantum physics and of its ability to…
Various quantum measurement procedures are analyzed and it is shown that under certain conditions they yield consistently {\em weak values} which might be very different from the eigenvalues, the allowed outcomes according to the standard…
Busch's theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleason's theorem. Here we show that a further generalisation is possible by reducing the number of quantum postulates used by Busch.…
A new relativistic quantum protocol is proposed allowing to implement the bit commitment scheme. The protocol is based on the idea that in the relativistic case the field propagation to the region of space accessible to measurement…
For a property $P$ and a sub-property $P'$, we say that $P$ is $P'$-partially testable with $q$ queries if there exists an algorithm that distinguishes, with high probability, inputs in $P'$ from inputs $\epsilon$-far from $P$ by using $q$…
One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particle-like \emph{or} a wave-like behaviour, but never both at the same time. These are mutually exclusive and…
This Colloquium examines the field of the EPR Gedankenexperiment, from the original paper of Einstein, Podolsky and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the…