Related papers: The Prime state and its quantum relatives
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…
Completely entangled quantum states are shown to factorize into tensor products of entangled states whose dimensions are powers of prime numbers. The entangled states of each prime-power dimension transform among themselves under a finite…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics…
We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity…
The physical regions (domains or basins) within the molecular structure are open systems that exchange charge between them and consequently house a fractional number of electrons (net charge). The natural framework describing the quantum…
From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack…
In this paper, we investigate a characterization of Quantum Mechanics by two physical principles based on general probabilistic theories. We first give the operationally motivated definition of the physical equivalence of states and…
Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
The N to M (M>N) universal quantum broadcasting of mixed states are proposed for qubits system. The broadcasting of mixed states is universal and optimal in the sense that the shrinking factor is independent of input state and achieves the…
We prove that the vast majority of symmetric states of qubits can be decomposed in a unique way into a superposition of spin 1/2 coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition…
We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can…
We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…
The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
We define and study the properties of ``squeezed quantum multiplets''. Ordinary multiplets are sets of $D$-orthonormal quantum states formed by superpositions of states squeezed along $D$ equally spaced directions in quadrature space. More…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement…