Related papers: High resolution quantization and entropy coding of…
Quantum metrology exploits quantum correlations in specially prepared entangled or other non-classical states to perform measurements that exceed the standard quantum limit. Typically though, such states are hard to engineer, particularly…
The aim of this paper is to study the continuity correction for barrier options in jump-diusion models. For this purpose, we express the pay-off a barrier option in terms of the maximum of the underlying process. We then condition with…
Quantitative analysis of discontinuity of basic characteristics of quantum states and channels is presented. First we consider general estimates for discontinuity jump (loss) of the von Neumann entropy for a given converging sequence of…
We analyze the strong noise limit of one-dimensional stochastic differential equations (SDEs). Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
We study the obtainment of closed-form formulas for the distribution of the jumps of a doubly-stochastic Poisson process. The problem is approached in two ways. On the one hand, we translate the problem to the computation of multiple…
Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied…
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
We investigate the problem of factorization of large numbers on a quantum computer which we imagine to be realized within a linear ion trap. We derive upper bounds on the size of the numbers that can be factorized on such a quantum…
When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…
In the context of quantum information theory, "quantization" of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of…
We study the homogenization for a class of non-symmetric pure jump Feller processes. The jump intensity involves periodic and aperiodic constituents, as well as oscillating and non-oscillating constituents. This means that the noise can…
We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is…
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used…
In a fundamental test of quantum mechanics, we have observed 228~000 quantum jumps of a single trapped and laser cooled $^{88}$Sr$^+$ ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of…
The problem of initializing phase in a quantum computing system is considered. The initialization of phases is a problem when the system is initially present in an entangled state and also in the application of the quantum gate…
The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…