scholarly journals Purification complexity without purifications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shan-Ming Ruan
Keyword(s):  
Fisher Information ◽  
Mixed State ◽  
Quantum Fisher Information ◽  
Quantum States ◽  
Density Matrices ◽  
Gaussian States ◽  
State Complexity ◽  
Quantum Operations ◽  
Fisher Information Metric ◽  
Information Metric

Abstract We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric (QFIM) on the space of density matrices as the complexity measure. Due to Uhlmann’s theorem, we show that the mixed-state complexity exactly equals the purification complexity measured by the Fubini-Study metric for purified states but without explicitly applying any purification. We also find the purification complexity is non-increasing under any trace-preserving quantum operations. We also study the mixed Gaussian states as an example to explicitly illustrate our conclusions for purification complexity.

scholarly journals Quantum Fisher Information for Density Matrices with Arbitrary Ranks

2014 ◽  
Vol 61 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Jing Liu ◽  
Xiao-Xing Jing ◽  
Wei Zhong ◽  
Xiao-Guang Wang
Keyword(s):  
Fisher Information ◽  
Quantum Fisher Information ◽  
Density Matrices

scholarly journals Holographic Fisher information metric in Schrödinger spacetime

2021 ◽  
Vol 136 (11) ◽  
Author(s):  
H. Dimov ◽  
I. N. Iliev ◽  
M. Radomirov ◽  
R. C. Rashkov ◽  
T. Vetsov
Keyword(s):  
Fisher Information ◽  
Fisher Information Metric ◽  
Information Metric

scholarly journals Fisher Concord: Efficiency of Quantum Measurement

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Nan Li ◽  
Shunlong Luo
Keyword(s):  
Fisher Information ◽  
Fisher Information Matrix ◽  
Symmetric Matrix ◽  
Information Matrix ◽  
Quantum Fisher Information ◽  
Quantum Measurements ◽  
Quantum States ◽  
Information Theoretic ◽  
Information Conservation ◽  
Relative Accessibility

AbstractBy comparing measurement-induced classical Fisher information of parameterized quantum states with quantum Fisher information,we study the notion of Fisher concord (as abbreviation of the concord between the classical and the quantum Fisher information), which is an information-theoretic measure of quantum states and quantum measurements based on both classical and quantum Fisher information. Fisher concord is defined by multiplying the inverse square root of quantum Fisher information matrix to measurement-induced classical Fisher information matrix on both sides, and quantifies the relative accessibility of parameter information from quantum measurements (alternatively, the efficiency of quantum measurements in extracting parameter information). It reduces to the ratio of the classical Fisher information to quantum Fisher information in any single parameter scenario. In general, Fisher concord is a symmetric matrix which depends on both quantum states and quantum measurements. Some basic properties of Fisher concord are elucidated. The significance of Fisher concord in quantifying the interplay between classicality and quantumness in parameter estimation and in characterizing the ef- ficiency of quantum measurements are illustrated through several examples, and some information conservation relations in terms of Fisher concord are exhibited.

scholarly journals Remote State Design for Efficient Quantum Metrology with Separable and Non-Teleporting States

2021 ◽  
Vol 3 (1) ◽  
pp. 228-241
Author(s):  
Rahul Raj ◽  
Shreya Banerjee ◽  
Prasanta K. Panigrahi
Keyword(s):  
Parameter Estimation ◽  
Quantum Information ◽  
Fisher Information ◽  
Quantum Information Processing ◽  
Quantum Fisher Information ◽  
Quantum Correlations ◽  
Quantum States ◽  
Quantum Metrology ◽  
High Quantum ◽  
Non Local

Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by the physical environment and the measurement scheme itself. Its quantification is necessary to find efficient measurement schemes and circumvent the non-desirable environmental effects. This has led to the intense investigation of quantum metrology, extending the Cramér–Rao bound to the quantum domain through quantum Fisher information. Among all quantum states, the separable ones have the least quantumness; being devoid of the fragile non-local correlations, the component states remain unaffected in local operations performed by any of the parties. Therefore, using these states for the remote design of quantum states with high quantum Fisher information can have diverse applications in quantum information processing; accurate parameter estimation being a prominent example, as the quantum information extraction solely depends on it. Here, we demonstrate that these separable states with the least quantumness can be made extremely useful in parameter estimation tasks, and further show even in the case of the shared channel inflicted with the amplitude damping noise and phase flip noise, there is a gain in Quantum Fisher information (QFI). We subsequently pointed out that the symmetric W states, incapable of perfectly teleporting an unknown quantum state, are highly effective for remotely designing quantum states with high quantum Fisher information.

scholarly journals Symmetric Logarithmic Derivative of Fermionic Gaussian States

2018 ◽  
Author(s):  
Angelo Carollo ◽  
Bernardo Spagnolo ◽  
Davide Valenti
Keyword(s):  
Fisher Information ◽  
Logarithmic Derivative ◽  
Quantum Fisher Information ◽  
Closed Form Expression ◽  
Quantum Metrology ◽  
Many Body ◽  
Form Expression ◽  
Gaussian States ◽  
Many Body Systems ◽  
Thermal States

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

scholarly journals Incompatibility in Multi-Parameter Quantum Metrology with Fermionic Gaussian States

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 34
Author(s):  
Angelo Carollo ◽  
Bernardo Spagnolo ◽  
Davide Valenti
Keyword(s):  
Fisher Information ◽  
Quantum Fisher Information ◽  
Spin Systems ◽  
Closed Form Expression ◽  
Quantum Metrology ◽  
Form Expression ◽  
Gaussian States ◽  
Optimal Measurement ◽  
Measurement Strategies ◽  
Thermal States

In this article we derive a closed form expression for the incompatibility condition in multi-parameter quantum metrology when the reference states are Fermionic Gaussian states. Together with the quantum Fisher information, the knowledge of the compatibility condition provides a way of designing optimal measurement strategies for multi-parameter quantum estimation. Applications range from quantum metrology with thermal states to non-equilibrium steady states with Fermionic and spin systems.

scholarly journals Appearance of Thermal Time

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Shigenori Tanaka
Keyword(s):  
Differential Geometry ◽  
Relaxation Process ◽  
Fisher Information ◽  
Basic Equation ◽  
Dynamical Process ◽  
Two Dimensional ◽  
Event Time ◽  
Fisher Information Metric ◽  
Intrinsic Correlation ◽  
Information Metric

AbstractIn this paper a viewpoint that time is an informational and thermal entity is presented. We consider a model for a simple relaxation process for which a relationship among event, time and temperature is mathematically formulated. It is then explicitly illustrated that temperature and time are statistically inferred through measurement of events. The probability distribution of the events thus provides an intrinsic correlation between temperature and time, which can relevantly be expressed in terms of the Fisher information metric. The two-dimensional differential geometry of temperature and time then leads us to a finding of a simple equation for the scalar curvature, $$R = -1$$ R = - 1 , in this case of relaxation process. This basic equation, in turn, may be regarded as characterizing a nonequilibrium dynamical process and having a solution given by the Fisher information metric. The time can then be interpreted so as to appear in a thermal way.

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