Related papers: Purification Complexity without Purifications
The geometry of quantum states has profound implications in quantum multiparameter estimation. While the Riemannian structure of quantum state space is well understood, the full understanding of the curvature structure of mixed quantum…
Starting from the observation that reversible processes cannot increase the purity of any input state, we study deterministic physical processes, which map a set of states to a set of pure states. Such a process must map any state to the…
Mutually unbiased measurements are a generalization of mutually unbiased bases in which the measurement operators need not to be rank one projectors. In a $d$-dimension space, the purity of measurement elements ranges from $1/d$ for the…
We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…
We discuss single adaptive measurements for the estimation of mixed quantum states of qubits. The results are compared to the optimal estimation schemes using collective measurements. We also demonstrate that the advantage of collective…
Consanguinity of entropy and complexity is pointed out through the example of coherent states of the group $SL(d+1,\C)$. Both are obtained from the K\"ahler potential of the underlying geometry of the sphere corresponding to the…
State-average calculations based on mixture of states are increasingly being exploited across chemistry and physics as versatile procedures for addressing excitations of quantum many-body systems. If not too many states should need to be…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
The Bures-Hall ensemble is a unique measure of density matrices that satisfies various distinguished properties in quantum information processing. In this work, we study the statistical behavior of entanglement over the Bures-Hall ensemble…
We introduce new formulations of the quantum Cram\'{e}r-Rao bound (QCRB) and the Holevo Cram\'{e}r-Rao bound (HCRB) in multi-parameter quantum metrology via purification, where we show their values for any mixed state are connected to that…
We propose a quantum algorithm for the purification of a generic mixed state $\rho$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii)…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We…
We propose a new generalised formalism for estimating the quantum phase uncertainty of pure and mixed continuous-variable quantum states and compare this with the phase uncertainty given by the quantum Fisher information. In order to…
We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…
We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than…
Accurate modeling of quantum systems interacting with environments requires addressing non-unitary dynamics, which significantly complicates computational approaches. In this work, we enhance an open quantum system (OQS) theory using…
Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…