Related papers: Eigenvalue Determination for Mixed Quantum States …
We investigate whether pure entangled states can be associated to a measurement basis in which all vectors are local unitary transformations of the original state. We prove that for bipartite states with a local dimension that is either $2,…
We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…
Local unitary equivalence is an important ingredient for quantifying and classifying entanglement. Verifying whether or not two quantum states are local unitary equivalent is a crucial problem, where only the case of multipartite pure…
We describe a subtle error which can appear in numerical calculations involving the spacing statistics of eigenvalues of random unitary matrices.
We analyze the entangling capabilities of unitary transformations $U$ acting on a bipartite $d_1\times d_2$-dimensional quantum system. To this aim we introduce an entangling power measure $e(U)$ given by the mean linear entropy produced…
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum…
Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
Fault-tolerant quantum computation can be achieved by creating constant-sized, entangled resource states and performing entangling measurements on subsets of their qubits. Linear optical quantum computers can be designed based on this…
The entanglement of eigenstates in two coupled, classically chaotic kicked tops is studied in dependence of their interaction strength. The transition from the non-interacting and unentangled system towards full random matrix behavior is…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state,…
It is very crucial to know that whether the quantum state generated in the experiment is entangled or not. In the literature, this topic was studied extensively and researchers proposed different approaches for the detection of mixed…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
We present a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices. This class…
When a subset of particles in an entangled state is measured, the state of the subset of unmeasured particles is determined by the outcome of the measurement. This first measurement may be thought of as a state preparation for the remaining…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
The equivalence of multipartite quantum mixed states under local unitary transformations is studied. A criterion for the equivalence of non-degenerate mixed multipartite quantum states under local unitary transformations is presented.
As one of the most intriguing intrinsic properties of quantum world, quantum superposition provokes great interests in its own generation. Oszmaniec [Phys. Rev. Lett. 116, 110403 (2016)] have proven that though a universal quantum machine…