Related papers: Quantifier elimination theory and maps which prese…
Quantum error mitigation techniques can reduce noise on current quantum hardware without the need for fault-tolerant quantum error correction. For instance, the quasiprobability method simulates a noise-free quantum computer using a noisy…
Comparison of statistical models (experiments) is an important branch of mathematical statistics, which gives deep insights in many aspects of foundation of statistics. So far, there are two quantum versions of the concept: Comparison with…
Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…
We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the…
Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new…
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
Quantum devices use qubits to represent information, which allows them to exploit important properties from quantum physics, specifically superposition and entanglement. As a result, quantum computers have the potential to outperform the…
We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that…
The ability of implementing quantum operations plays fundamental role in manipulating quantum systems. Creation and annihilation operators which transform a quantum state to another by adding or subtracting a particle are crucial of…
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present…
We reconstruct finite-dimensional quantum theory from categorical principles. That is, we provide properties ensuring that a given physical theory described by a dagger compact category in which one may `discard' objects is equivalent to a…
We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs and some theorems about constructible subsets of real…
Semiclassical techniques have proven to be a very powerful method to extract physical effects from different quantum theories. Therefore, it is expected that in the near future they will play a very prominent role in the context of quantum…
We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically…
It is shown here how the semiclassical theory of electrical susceptibility can be extended to the case in which both radiation and matter are quantized. This is done specifically for the cases of linear and second order susceptibilities.…
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
We investigate variational problems in quantum thermodynamics at positive temperature, in which admissible states are constrained by prescribed outcomes of a finite set of measurements. We solve a problem raised by the recent work [Liu,…