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Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed…
A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…
We initially consider a quantum system consisting of two qubits, which can be in one of two nonorthogonal states, \Psi_0 or \Psi_1. We distribute the qubits to two parties, Alice and Bob. They each measure their qubit and then compare their…
We study genuine tripartite entanglement and multipartite entanglement of arbitrary $n$-partite quantum states by using the representations with generalized Pauli operators of a density matrices. While the usual Bloch representation of a…
How to achieve an arbitrary real-valued probability amplitude in the general single-partite or multipartite quantum system without measuring any other quantum state's probability amplitude? How to achieve an arbitrary real-valued…
In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best,…
In fault-tolerant quantum computation, the preparation of logical states is a ubiquitous subroutine, yet significant challenges persist even for the simplest states required. In the present work, we present a unitary, scalable,…
Qudits with local dimension $d>2$ can have unique structure and uses that qubits ($d=2$) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
We find the allowed complex numbers associated with the inner product of N equally separated pure quantum states. The allowed areas on the unitary complex plane have the form of petals. A point inside the petal-shape represents a set of N…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
Multi-qudit systems are studied in tomographic probability representations of quantum qudit states. Results of calculations for Bell-type numbers within the framework of classical probability theory and in quantum tomography are compared.…
Robust, accurate and efficient quantum tomography is key for future quantum technologies. Traditional methods are impractical for even medium sized systems and are not robust against noise and errors. Here we report on an experimental…
Euclidean volume ratios between quantum states with positive partial transpose and all quantum states in bipartite systems are investigated. These ratios allow a quantitative exploration of the typicality of entanglement and of its…
We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and…
The field of neural quantum states has recently experienced a tremendous progress, making them a competitive tool of computational quantum many-body physics. However, their largest achievements to date mostly concern interacting spin…
We introduce and investigate a data access model (approximate sample and query) that is satisfiable by the preparation and measurement of block encoded states, as well as in contexts such as classical quantum circuit simulation or Pauli…
Characterizing large noisy multiparty quantum states using genuine multiparty entanglement is a challenging task. In this paper, we calculate lower bounds of genuine multiparty entanglement localized over a chosen multiparty subsystem of…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared…