Related papers: Randomizing quantum states in Shatten $p$-norms

In quantum estimation theory and quantum tomography, the quantum state obtained by sampling converges to the `true' unknown density matrix under topologies that are different from the natural notion of distance in the space of quantum…

In this paper we consider symmetric, positive semidefinite (SPSD) matrix $A$ and present two algorithms for computing the $p$-Schatten norm $\|A\|_p$. The first algorithm works for any SPSD matrix $A$. The second algorithm works for…

The Schatten-$p$ quasi-norm with $p\in(0,1)$ has recently gained considerable attention in various low-rank matrix estimation problems offering significant benefits over relevant convex heuristics such as the nuclear norm. However, due to…

Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional…

Working with a rather general notion of independence, we provide a transference method which allows to compare the p-norm of sums of independent copies with the p-norm of sums of free copies. Our main technique is to construct explicit…

The concept of $\e$-randomizing quantum channels has been introduced by Hayden, Leung, Shor and Winter in connection with approximately encrypting quantum states. They proved using a discretization argument that sets of roughly $d \log d$…

We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…

We consider the quantum complexity of computing Schatten $p$-norms and related quantities, and find that the problem of estimating these quantities is closely related to the one clean qubit model of computation. We show that the problem of…

Efficient measures to determine similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be…

The quantum speed limit is a fundamental upper bound on the speed of quantum evolution. However, the actual mathematical expression of this fundamental limit depends on the choice of a measure of distinguishability of quantum states. We…

The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…

We propose a quantum optical device to experimentally realize quantum processes, which perform the regularization of the---in general highly singular---Glauber-Sudarshan $P$~functions of arbitrary quantum states before their application…

We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…

We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schatten spaces. We establish several…

Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in Von Neumann entropy to…

We develop two general approaches to characterising the manipulation of quantum states by means of probabilistic protocols constrained by the limitations of some quantum resource theory. First, we give a general necessary condition for the…

We investigate the violation of Bell-type inequalities for two-qubit Werner-like states parametrized by the positive parameter 0<p<1. We use an unbalanced homodyne detection scheme to obtain the quantum mechanical probabilities. A violation…

We develop a new refinement of the Kato's inequality and using this refinement we obtain several upper bounds for the numerical radius of a bounded linear operator as well as the product of operators, which improve the well known existing…

Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p in P or from a distribution q in Q and wants to decide from which set the…

Producing quantum states at random has become increasingly important in modern quantum science, with applications both theoretical and practical. In particular, ensembles of such randomly-distributed, but pure, quantum states underly our…