scholarly journals Probing quantum state space: does one have to learn everything to learn something?

2017 ◽  
Vol 473 (2201) ◽  
pp. 20160866 ◽  
Author(s):  
Claudio Carmeli ◽  
Teiko Heinosaari ◽  
Jussi Schultz ◽  
Alessandro Toigo
Keyword(s):  
State Space ◽  
Quantum System ◽  
Quantum State ◽  
The State ◽  
Membership Problem ◽  
Complete Measurement ◽  
Alternative Means ◽  
Informational Completeness ◽  
Set Up

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task.

Characterizations of symmetric monotone metrics on the state space of quantum systems

2006 ◽  
Vol 6 (7) ◽  
pp. 597-605
Author(s):  
F. Hansen
Keyword(s):  
State Space ◽  
Quantum System ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Classical Case ◽  
Riemannian Metric ◽  
Quantum Systems ◽  
The State ◽  
Stochastic Mappings

The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, initiated by Morozova, Chentsov and Petz, of these metrics by providing a closed and tractable formula for the set of Morozova-Chentsov functions. In addition, we provide a continuously increasing bridge between the smallest and largest symmetric monotone metrics.

scholarly journals Image Thresholding Segmentation on Quantum State Space

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 728 ◽  
Author(s):  
Xiangluo Wang ◽  
Chunlei Yang ◽  
Guo-Sen Xie ◽  
Zhonghua Liu
Keyword(s):  
State Space ◽  
Quantum State ◽  
Structural Characteristics ◽  
The State ◽  
Entropy Maximization ◽  
Image Thresholding ◽  
Optimal Thresholds ◽  
Segmented Images ◽  
Computation Speed

Aiming to implement image segmentation precisely and efficiently, we exploit new ways to encode images and achieve the optimal thresholding on quantum state space. Firstly, the state vector and density matrix are adopted for the representation of pixel intensities and their probability distribution, respectively. Then, the method based on global quantum entropy maximization (GQEM) is proposed, which has an equivalent object function to Otsu’s, but gives a more explicit physical interpretation of image thresholding in the language of quantum mechanics. To reduce the time consumption for searching for optimal thresholds, the method of quantum lossy-encoding-based entropy maximization (QLEEM) is presented, in which the eigenvalues of density matrices can give direct clues for thresholding, and then, the process of optimal searching can be avoided. Meanwhile, the QLEEM algorithm achieves two additional effects: (1) the upper bound of the thresholding level can be implicitly determined according to the eigenvalues; and (2) the proposed approaches ensure that the local information in images is retained as much as possible, and simultaneously, the inter-class separability is maximized in the segmented images. Both of them contribute to the structural characteristics of images, which the human visual system is highly adapted to extract. Experimental results show that the proposed methods are able to achieve a competitive quality of thresholding and the fastest computation speed compared with the state-of-the-art methods.

scholarly journals ON THE CURVATURE OF A CERTAIN RIEMANNIAN SPACE OF MATRICES

2000 ◽  
Vol 03 (02) ◽  
pp. 199-212 ◽  
Author(s):  
PETER W. MICHOR ◽  
DÉNES PETZ ◽  
ATTILA ANDAI
Keyword(s):  
Scalar Curvature ◽  
State Space ◽  
Quantum System ◽  
Curvature Tensor ◽  
Riemannian Space ◽  
Riemannian Metric ◽  
Positive Definite ◽  
The State ◽  
Inner Product ◽  
Positive Definite Matrices

Positive definite matrices of trace 1 describe the state space of a finite quantum system. This manifold can be endowed by the physically relevant Bogoliubov–Kubo–Mori inner product as a Riemannian metric. In this paper the curvature tensor and the scalar curvature are computed.

scholarly journals The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 485
Author(s):  
Christopher Eltschka ◽  
Marcus Huber ◽  
Simon Morelli ◽  
Jens Siewert
Keyword(s):  
State Space ◽  
Quantum System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The State ◽  
Level System ◽  
Three Dimensional Model ◽  
System A ◽  
Dimensional State Space ◽  
Geometric Intuition

Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit). However, already for a three-level system (qutrit) the state space has eight dimensions, so that its complexity exceeds the grasp of our three-dimensional space of experience. This is unfortunate, given that the geometric object describing the state space of a qutrit has a much richer structure and is in many ways more representative for a general quantum system than a qubit. In this work we demonstrate that, based on the Bloch representation of quantum states, it is possible to construct a three dimensional model for the qutrit state space that captures most of the essential geometric features of the latter. Besides being of indisputable theoretical value, this opens the door to a new type of representation, thus extending our geometric intuition beyond the simplest quantum systems.

A NEW METHOD TO CALCULATE THE INCONCLUSIVE COEFFICIENTS IN THE QUANTUM STATE DISCRIMINATION

2011 ◽  
Vol 22 (02) ◽  
pp. 95-105 ◽  
Author(s):  
TATIANE EVANGELISTA ◽  
CARLILE LAVOR ◽  
WILSON R. M. RABELO
Keyword(s):  
Quantum System ◽  
Quantum State ◽  
Quantum Information Processing ◽  
The State ◽  
New Method ◽  
Quantum State Discrimination ◽  
State Discrimination ◽  
Different Dimensions ◽  
Roots Of A Polynomial

The problem of determining the state of a quantum system is a central task in any quantum information processing. However, there are limitations imposed by quantum mechanics on the possibilities to determine the state of a quantum system. For example, nonorthogonal states cannot be discriminated perfectly. In this paper, we propose a new method to calculate the inconclusive coefficients based on the solution of a quadratic system, replacing the determination of the roots of a polynomial of degree 8, used in an algorithm to quantum state discrimination previously defined in the literature. The new method simplifies the calculation of the inconclusive coefficients and can be extended very easily to any dimension. The method was written in Matlab and successfully applied to problems with different dimensions.

Symmetries of the Quantum State Space and Group Representations

1998 ◽  
Vol 10 (07) ◽  
pp. 893-924 ◽  
Author(s):  
Gianni Cassinelli ◽  
Ernesto de Vito ◽  
Pekka Lahti ◽  
Alberto Levrero
Keyword(s):  
State Space ◽  
Quantum System ◽  
Symmetry Group ◽  
Quantum State ◽  
Lie Group ◽  
Universal Covering ◽  
Unitary Representations ◽  
Group Representations ◽  
Simply Connected ◽  
Connected Lie Group

The homomorphisms of a connected Lie group G into the symmetry group of a quantum system are classified in terms of unitary representations of a simply connected Lie group associated with G. Moreover, an explicit description of the T-multipliers of G is obtained in terms of the ℝ-multipliers of the universal covering G* of G and the characters of G*. As an application, the Poincaré group and the Galilei group, both in 3+1 and 2+1 dimensions, are considered.

scholarly journals BOUNDARY UNITARITY AND THE BLACK HOLE INFORMATION PARADOX

2013 ◽  
Vol 22 (12) ◽  
pp. 1342002 ◽  
Author(s):  
TED JACOBSON
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Tensor Product ◽  
State Space ◽  
Event Horizon ◽  
Quantum State ◽  
Degrees Of Freedom ◽  
The State ◽  
S Matrix ◽  
Black Hole Information

Both AdS/CFT duality and more general reasoning from quantum gravity point to a rich collection of boundary observables that always evolve unitarily. The physical quantum gravity states described by these observables must be solutions of the spatial diffeomorphism and Wheeler–De Witt constraints, which implies that the state space does not factorize into a tensor product of localized degrees of freedom. The "firewall" argument that unitarity of black hole S-matrix implies the presence of a highly excited quantum state near the horizon is based on such a factorization, hence is not applicable in quantum gravity. In fact, there appears to be no conflict between boundary unitarity and regularity of the event horizon.

MIDC Role in Infrastructural Development in Navi Mumbai

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Prashant H. Bhagat
Keyword(s):  
Industrial Development ◽  
Industrial Sector ◽  
Vital Role ◽  
The State ◽  
Infrastructure Development ◽  
Industrial Areas ◽  
Industrial Estates ◽  
Development Corporation ◽  
Set Up ◽  
Industrial Development Corporation

The BID (Board of Industrial Development) framed the legislation and it was introduced before the state legislation and passed in the form of Maharashtra Industrial Act which gave birth to Maharashtra Industrial Development Corporation (MIDC), as a separate corporation on August 1, 1962. The BID was the first personnel strength of MIDC. A small ceremony at Wagle Estate Thane, under the Chairmanship of the Chief Minister Shri Y.B. Chavan, marked the birth of MIDC on August 1, 1962. The Board of Industrial Development during its existence between October 1, 1960 and August 1, 1962 has done enough spade work to identify the locations for setting up industrial areas in different parts of the state. Thus, right in the first year of establishment MIDC came up with 14 industrial areas, to initiate action for infrastructure and help entrepreneurs set up the industrial units in those areas. Maharashtra Industrial Development Corporation is the nodal industrial infrastructure development agency of the Maharashtra Government with the basic objective of setting up industrial areas with a provision of industrial infrastructure all over the state for planned and systematic industrial development. MIDC is an innovative, professionally managed, and user friendly organization that provides the world industrial infrastructure. MIDC has played a vital role in the development of industrial infrastructure in the state of Maharashtra. As the state steps into the next millennium, MIDC lives up to its motto Udyamat Sakal Samruddhi i.e., prosperity to all through industrialization. Indeed, in the endeavor of the state to retain its prime position in the industrial sector, MIDC has played a pivotal role in the last 35 years. MIDC has developed 268 industrial estates across the state which spread over 52653 hectares of land. The growth of the Corporation, achieved in the various fields, during the last three years, could be gauged from the fact that the area currently in possession of MIDC has doubled from 25,000 hectares in 1995.

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