Related papers: Symmetric functions of qubits in an unknown basis

Current quantum computers have the potential to overcome classical computational methods, however, the capability of the algorithms that can be executed on noisy intermediate-scale quantum devices is limited due to hardware imperfections.…

Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…

Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…

For quantum field theories with global symmetry, we can study the behavior of the partition function with the background gauge field to diagnose different quantum phases. For the case of discrete symmetries, we find that the…

This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…

Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…

We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability…

In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…

The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…

We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…

We present a divide-and-conquer approach to deterministically prepare Dicke states $\lvert D_k^n\rangle$ (i.e., equal-weight superpositions of all $n$-qubit states with Hamming Weight $k$) on quantum computers. In an experimental evaluation…

We consider a Quantum Computer with n quantum-bits (`qubits'), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we suggest a quantification for the property…

The physics of a quantum system with many degrees of freedom is often approximated by downfolding: most of the degrees of freedom are "folded into" a much smaller number of degrees of freedom, resulting in an effective Hamiltonian that…

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…

We consider the problem of determining the weights of a quantum ensemble. That is to say, given a quantum system that is in a set of possible known states according to an unknown probability law, we give strategies to estimate the…

We propose and experimentally realize an algorithmic benchmark that demonstrates coherent control with a sequence of quantum operations that first generates and then decodes the cat state (|000...>+|111...>)/sqrt(2) to the standard initial…

We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…

We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…

We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…

We construct a probabilistic quantum cloning machine by a general unitary-reduction operation. With a postselection of the measurement results, the machine yields faithful copies of the input states. It is shown that the states secretly…