Quantum mutual information matrices

2017 ◽  
Vol 15 (01) ◽  
pp. 1750005
Author(s):  
Feng Liu
Keyword(s):  
Mutual Information ◽  
Information Matrix ◽  
Positive Semidefinite ◽  
Text Entry ◽  
Classical Counterpart ◽  
State Formula ◽  
Quantum Mutual Information ◽  
Multipartite States ◽  
Information Matrices

For any [Formula: see text]-partite state [Formula: see text], we define its quantum mutual information matrix as an [Formula: see text][Formula: see text][Formula: see text][Formula: see text][Formula: see text] matrix whose [Formula: see text]-entry is given by quantum mutual information [Formula: see text]. Although each entry of quantum mutual information matrix, like its classical counterpart, is also used to measure bipartite correlations, the similarity ends here: quantum mutual information matrices are not always positive semidefinite even for collections of up to 3-partite states. In this work, we define the genuine n-partite mutual information which can be easily calculated. This definition is symmetric, nonnegative, bounded and more accurate for measuring multipartite states.

Gaussian–Rényi-2 correlations hierarchy in optomechanics

2021 ◽  
pp. 2150004
Author(s):  
B. Maroufi ◽  
J. El Qars ◽  
M. Daoud
Keyword(s):  
Mutual Information ◽  
Thermal Effects ◽  
Freezing Behavior ◽  
The State ◽  
Gaussian State ◽  
Wide Range ◽  
State Formula ◽  
Quantum Steering ◽  
Quantum Mutual Information ◽  
Hierarchical Relation

In a two-mode Gaussian state [Formula: see text], we report on stationary evolution of three measures of correlations defined via the Rényi-2 entropy, i.e. quantum mutual information (QMI) [Formula: see text], the Gaussian–Rényi-2 entanglement (GR2E) [Formula: see text] and Gaussian quantum steering (GQS) [Formula: see text]. We evaluate analytical expression of the covariance matrix fully describing the state [Formula: see text]. Further, we study, under influences of parameters characterizing the state at hand and its environment, the behavior of the three considered measures. We find that quantum steering [Formula: see text] is always upper bounded by (GR2E) [Formula: see text], which in turn is found always upper bounded by half of the QMI [Formula: see text]. This therefore satisfies the hierarchical relation [Formula: see text] established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett.117 (2016) 220502]. Importantly, we find that both GR2E [Formula: see text] and GQS [Formula: see text] are strongly affected by the thermal effects. Remarkably, when the GR2E [Formula: see text] thoroughly vanishes, the GMI [Formula: see text] exhibits a freezing behavior, and seems to be captured within a wide range of temperature.

scholarly journals CALCULATING A MAXIMIZER FOR QUANTUM MUTUAL INFORMATION

2008 ◽  
Vol 06 (supp01) ◽  
pp. 745-750 ◽  
Author(s):  
T. C. DORLAS ◽  
C. MORGAN
Keyword(s):  
Mutual Information ◽  
State Capacity ◽  
Convex Combination ◽  
Product State ◽  
Not Given ◽  
Classical Information ◽  
Amplitude Damping Channel ◽  
Quantum Amplitude ◽  
Memoryless Channels ◽  
Quantum Mutual Information

We obtain a maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel. We also consider the product state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels.

Information Matrices in Latent-Variable Models

1989 ◽  
Vol 14 (4) ◽  
pp. 335-350 ◽  
Author(s):  
Robert J. Mislevy ◽  
Kathleen M. Sheehan
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Information Matrix ◽  
Missing Information ◽  
Variable Model ◽  
Related Information ◽  
Expected Information ◽  
The Difference ◽  
Information Matrices ◽  
Practical Implications

The Fisher, or expected, information matrix for the parameters in a latent-variable model is bounded from above by the information that would be obtained if the values of the latent variables could also be observed. The difference between this upper bound and the information in the observed data is the “missing information.” This paper explicates the structure of the expected information matrix and related information matrices, and characterizes the degree to which missing information can be recovered by exploiting collateral variables for respondents. The results are illustrated in the context of item response theory models, and practical implications are discussed.

scholarly journals Rényi generalizations of the conditional quantum mutual information

2015 ◽  
Vol 56 (2) ◽  
pp. 022205 ◽  
Author(s):  
Mario Berta ◽  
Kaushik P. Seshadreesan ◽  
Mark M. Wilde
Keyword(s):  
Mutual Information ◽  
Quantum Mutual Information

Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices

2009 ◽  
Vol 59 (6) ◽  
Author(s):  
Radoslav Harman ◽  
Mária Trnovská
Keyword(s):  
Convex Hull ◽  
Positive Semidefinite ◽  
Optimal Designs ◽  
Quadratic Model ◽  
Positive Semidefinite Matrices ◽  
Multiplicative Algorithm ◽  
Finite Set ◽  
Designs Of Experiments ◽  
Information Matrices ◽  
Proof Of Convergence

AbstractIn the paper we solve the problem of D ℋ-optimal design on a discrete experimental domain, which is formally equivalent to maximizing determinant on the convex hull of a finite set of positive semidefinite matrices. The problem of D ℋ-optimality covers many special design settings, e.g., the D-optimal experimental design for multivariate regression models. For D ℋ-optimal designs we prove several theorems generalizing known properties of standard D-optimality. Moreover, we show that D ℋ-optimal designs can be numerically computed using a multiplicative algorithm, for which we give a proof of convergence. We illustrate the results on the problem of D-optimal augmentation of independent regression trials for the quadratic model on a rectangular grid of points in the plane.

scholarly journals The locking-decoding frontier for generic dynamics

2013 ◽  
Vol 469 (2159) ◽  
pp. 20130289 ◽  
Author(s):  
Frédéric Dupuis ◽  
Jan Florjanczyk ◽  
Patrick Hayden ◽  
Debbie Leung
Keyword(s):  
Mutual Information ◽  
Quantum Key Distribution ◽  
Black Hole Physics ◽  
Quantum Systems ◽  
Classical Information ◽  
Accessible Information ◽  
Generic Dynamics ◽  
Quantum Mutual Information ◽  
Logarithmic Number ◽  
Quantum Key Distribution Protocol

It is known that the maximum classical mutual information, which can be achieved between measurements on pairs of quantum systems, can drastically underestimate the quantum mutual information between them. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might yield only outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. While previous works had always assumed a uniform message, we assume only a min-entropy bound and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. Finally, we exhibit a quantum key distribution protocol that is ‘secure’ in the sense of accessible information but in which leakage of even a logarithmic number of bits compromises the secrecy of all others.

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