Related papers: Dichotomic probability representation of quantum s…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this…
The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we we introduce a quantifier of complexity of…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph, Nature Physics 8, 475 (2012)), models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have…
A general framework of quantum state amplification using the language of quantum state transformation is given systematically for the first time. The concept of amplification of quantum states is defined specifically and the amplification…
We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously…
This letter examines the consequences of a recently proposed modification of the postulate of equal {\it a priori} probability in quantum statistical mechanics. This modification, called the {\it quantum microcanonical postulate} (QMP),…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
A representation of heterogeneous stochastic populations that are composed of sub-populations with different levels of distinguishability is introduced together with an analysis of its properties. It is demonstrated that any instance of…
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications…
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…
A $\widetilde{Q}-$representation of real numbers is introduced as a generalization of the $p-$adic and $Q-$representations. It is shown that the $\widetilde{Q}-$representation may be used as a convenient tool for the construction and study…
The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary…
We investigate the optimal convex approximation of the quantum state with respect to a set of available states. By isometric transformation, we have presented the general mathematical model and its solutions together with a triple…
Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required…