Related papers: Partition of unity with mixed quantum states
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We find that a class of entanglement measures for bipartite pure state can be expressed by the average values of quantum operators, which are related to any complete basis of one partite operator space. Two specific examples are given based…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
In this article we introduce a novel quantum state, the perfect quantum optical vortex state which exhibits a highly localised distribution along a ring in the quadrature space. We examine its nonclassical properties using the Wigner…
Any set of pure states living in an given Hilbert space possesses a natural and unique metric --the Haar measure-- on the group $U(N)$ of unitary matrices. However, there is no specific measure induced on the set of eigenvalues $\Delta$ of…
In this article we extend results from our previous work [Bendersky, de la Torre, Senno, Figueira and Ac\'in, Phys. Rev. Lett. 116, 230406 (2016)] by providing a protocol to distinguish in finite time and with arbitrarily high success…
We investigate the undetermined sets consisting of two-level, multi-partite pure quantum states, whose reduced density matrices give absolutely no information of their original states. Two approached of finding these quantum states are…
Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…
The canonical Schmidt decomposition of quantum states is discussed and its implementation to the Quantum Computation Simulator is outlined. In particular, the semiorder relation in the space of quantum states induced by the lexicographic…
X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement,…
Fidelity plays an important role in measuring distances between pairs of quantum states, of single as well as multiparty systems. Based on the concept of fidelity, we introduce a physical quantity, shared purity, for arbitrary pure or mixed…
The computable measure of the mixed-state entanglement, the negativity, is shown to admit a clear geometrical interpretation, when applied to Schmidt-correlated (SC) states: the negativity of a SC state equals a distance of the state from a…
Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart…
In this paper, we consider the problem of how to quantify entanglement for any multipartite quantum states. For bipartite pure states partial entropy is a good entanglement measure. By using partial entropy, we firstly introduce the…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…