Related papers: Quantum Operations, State Transformations and Prob…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
The problem of quantum state discrimination, which is a foundational aspect of quantum information theory, and its relation to the theory of majorization are discussed. The purpose of this study is to review different approaches to the…
We demonstrate that local transformations on a composite quantum system can be enhanced in the presence of certain entangled states. These extra states act much like catalysts in a chemical reaction: they allow otherwise impossible local…
A measure of entanglement production by quantum operations is suggested. This measure is general, being valid for operations over pure states as well as over mixed states, for equilibrium as well as for nonequilibrium processes. The measure…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
The preparation of quantum states, especially cooling, is a fundamental technology for nanoscale devices. The past decade has seen important results related to both the limits of state transformation and the limits to their efficiency --…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique…
The most basic local conversion is local operations and classical communications (LOCC), which is also the most natural restriction in quantum information processing. We investigate the conversions between the ground states in quantum…
The problem of of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices describing N--dimensional…
Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a…
The effect of filtering operation with respect to purification and concentration of entanglement in quantum states are discussed in this paper. It is shown, through examples, that the local action of the filtering operator on a part of the…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
The remarkable phenomenon of catalyst tells us that adding a catalyst could help state transformation. In this paper, we consider the problem of catalyst-assisted probabilistic coherence distillation for mixed states under strictly…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
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 quantum nature of bulk ensemble NMR quantum computing --the center of recent heated debate, is addressed. Concepts of the mixed state and entanglement are examined, and the data in a 2 qubit liquid NMR quantum computation are analyzed.…
We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms considered in the canonical decomposition. Our result relies on the fact that states which are mixed by…