Related papers: Eigenvalue Determination for Mixed Quantum States …
The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…
We present a non perturbative calculation technique providing the mixed moments of the overlaps between the eigenvectors of two large quantum Hamiltonians: $\hat{H}_0$ and $\hat{H}_0+\hat{W}$, where $\hat{H}_0$ is deterministic and…
Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown…
For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each…
Efficient overlap estimation of high-dimensional quantum states is an important task in quantum information and a core element in computational speedups of quantum machine learning. Here we experimentally demonstrate the SWAP test that…
Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of mixed states. It is shown that two states in this class are…
We investigate how to experimentally detect a recently proposed measure to quantify macroscopic quantum superpositions [Phys. Rev. Lett. 106, 220401 (2011)], namely, "macroscopic quantumness" $\mathcal{I}$. Schemes based on overlap…
We give necessary conditions for the mixing problem in bipartite case, which are independent of eigenvalues and based on algebraic-geometric invariants of the bipartite states. One implication of our results is that for some special…
The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of different observables and to analyze the measurement results statistically. Here we show that the…
Experimentally, the imaginary parts of complex weak values are obtained from the response of the system to small unitary phase shifts generated by the target observable. The complex conditional probabilities obtained from weak measurements…
We investigate the equivalence of quantum mixed states under local unitary transformations. For a class of rank-two mixed states, a sufficient and necessary condition of local equivalence is obtained by giving a complete set of invariants…
It is a fundamental consequence of the superposition principle for quantum states that there must exist non-orthogonal states, that is states that, although different, have a non-zero overlap. This finite overlap means that there is no way…
The properties of mixed eigenstates in a generic quantum system with classical counterpart that has mixed-type phase space, although important to understand several fundamental questions that arise in both theoretical and experimental…
The overlap measurement scheme accomplishes to evaluate the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon…
The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary…
We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within…
The task of changing the overlap between two quantum states can not be performed by making use of a unitary evolution only. However, by means of a unitary-reduction process it can be probabilistically modified. Here we study in detail the…
We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint density of the singular values and of the eigenvalues of complex random matrices which are bi-unitarily invariant (also known as…