scholarly journals Information Geometry of Randomized Quantum State Tomography

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 609
Author(s):  
Akio Fujiwara ◽  
Koichi Yamagata
Keyword(s):  
Quantum State ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Information Geometry ◽  
Likelihood Method ◽  
Mutually Unbiased Bases ◽  
Quantum State Tomography ◽  
Unknown Quantum State ◽  
State Tomography ◽  
Insight Into

Suppose that a d-dimensional Hilbert space H ≃ C d admits a full set of mutually unbiased bases | 1 ( a ) 〉 , ⋯ , | d ( a ) 〉 , where a = 1 , ⋯ , d + 1 . A randomized quantum state tomography is a scheme for estimating an unknown quantum state on H through iterative applications of measurements M ( a ) = | 1 ( a ) 〉 〈 1 ( a ) | , ⋯ , | d ( a ) 〉 〈 d ( a ) | for a = 1 , ⋯ , d + 1 , where the numbers of applications of these measurements are random variables. We show that the space of the resulting probability distributions enjoys a mutually orthogonal dualistic foliation structure, which provides us with a simple geometrical insight into the maximum likelihood method for the quantum state tomography.

scholarly journals A scalable maximum likelihood method for quantum state tomography

2013 ◽  
Vol 15 (12) ◽  
pp. 125004 ◽  
Author(s):  
T Baumgratz ◽  
A Nüßeler ◽  
M Cramer ◽  
M B Plenio
Keyword(s):  
Maximum Likelihood ◽  
Quantum State ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Quantum State Tomography ◽  
State Tomography

scholarly journals Adaptive quantum state tomography with neural networks

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yihui Quek ◽  
Stanislav Fort ◽  
Hui Khoon Ng
Keyword(s):  
Machine Learning ◽  
Quantum State ◽  
The State ◽  
Learning To Learn ◽  
Seamless Integration ◽  
Quantum State Tomography ◽  
Flexible Machine ◽  
Meta Learning ◽  
Long Time ◽  
State Tomography

AbstractCurrent algorithms for quantum state tomography (QST) are costly both on the experimental front, requiring measurement of many copies of the state, and on the classical computational front, needing a long time to analyze the gathered data. Here, we introduce neural adaptive quantum state tomography (NAQT), a fast, flexible machine-learning-based algorithm for QST that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. As in other adaptive QST schemes, measurement adaptation makes use of the information gathered from previous measured copies of the state to perform a targeted sensing of the next copy, maximizing the information gathered from that next copy. Our NAQT approach allows for a rapid and seamless integration of measurement adaptation and statistical inference, using a neural-network replacement of the standard Bayes’ update, to obtain the best estimate of the state. Our algorithm, which falls into the machine learning subfield of “meta-learning” (in effect “learning to learn” about quantum states), does not require any ansatz about the form of the state to be estimated. Despite this generality, it can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems and potential speed-ups if provided with additional structure, such as a state ansatz.

scholarly journals Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source

Heliyon ◽  
2021 ◽  
pp. e07384
Author(s):  
Ali Motazedifard ◽  
S.A. Madani ◽  
J.J. Dashkasan ◽  
N.S. Vayaghan
Keyword(s):  
Quantum State ◽  
Type Ii ◽  
Quantum State Tomography ◽  
State Tomography

scholarly journals State-independent quantum state tomography by photon-number-resolving measurements

Optica ◽  
2019 ◽  
Vol 6 (10) ◽  
pp. 1356 ◽  
Author(s):  
Rajveer Nehra ◽  
Aye Win ◽  
Miller Eaton ◽  
Reihaneh Shahrokhshahi ◽  
Niranjan Sridhar ◽  
...  
Keyword(s):  
Quantum State ◽  
Photon Number ◽  
Quantum State Tomography ◽  
State Tomography

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

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