Related papers: How to mix a density matrix
A unified approach to parametrization of the mixing matrix for $N$ generations is developed. This approach not only has a clear geometrical underpinning but also has the advantage of being economical and recursive and leads in a natural way…
Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the…
We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the…
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…
Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is…
Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
The pure states that can be uniquely determined among all (UDA) states by their marginals are essential to efficient quantum state tomography. We generalize the UDA states from the context of pure states to that of arbitrary (no matter pure…
We present a novel algorithm to compute the density of states, which is proven to converge to the correct result. The algorithm is very general and can be applied to a wide range of models, in the frameworks of Statistical Mechanics and…
A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the…
In recent years, mixup regularization has gained popularity as an effective way to improve the generalization performance of deep learning models by training on convex combinations of training data. While many mixup variants have been…
By applying the supersymmetric approach we rigorously prove smoothness of the averaged density of states for a three dimensional random band matrix ensemble, in the limit of infinite volume and fixed band width. We also prove that the…
We introduce and carefully study a natural probability measure over the numerical range of a complex matrix $A \in M_n(\C)$. This numerical measure $\mu_A$ can be defined as the law of the random variable $<AX,X> \in \C$ when the vector $X…
We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in the system and the resultant closed subsector, which is naturally associated with the radial sector of the theory. The density of radial…
We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…
A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
New inequalities for tomographic probability distributions and density matrices of qutrit states are obtained by means of generalization of qubit portrait method. The approach based on the qudit portrait method to get new entropic…