Quaternion Representation and Symplectic Spin Tomography

Fedorov, Aleksey K.; Kiktenko, Evgeniy O.

doi:10.1007/s10946-013-9378-z

Cited by 6 publications

(5 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the probability representation of quantum mechanics is most oriented to continuousvariable systems, the discrete case is also of interest. It concerns primarily the qubit state tomography, which is relevant for quantum computing, quantum cryptography, and the related fields [35,36]. In this subsection, we demonstrate how several basic quantum processes acting on a qubit look like from a tomographic standpoint.…”

Section: Qubit Operationsmentioning

confidence: 99%

Quantum process in probability representation of quantum mechanics

Przhiyalkovskiy¹

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposition for the projection to a certain basis state and a Gaussian-type projection is demonstrated as well as qubit ﬂipping and amplitude damping processes.

show abstract

Section: Qubit Operationsmentioning

confidence: 99%

Quantum process in probability representation of quantum mechanics

Przhiyalkovskiy¹

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Here α, β ∈ C are the Cayley-Klein parameters. In U ∈ SU(2) case the Euler angles [6] and quaternions [7] can be used for representation of tomograms [30].…”

Section: Quantum Tomographymentioning

confidence: 99%

“…On the other hand, quantum tomography is an original picture of quantum mechanics, where quantum states are described in terms of nonnegative probability distributions functions [5]- [7]. Quantum tomography is equivalent to other approaches to quantum mechanics, and tomograms are directly related to quasi-probability distribution functions [8]- [9].…”

Section: Introductionmentioning

confidence: 99%

Tomographic causal analysis of two-qubit states and tomographic discord

Kiktenko¹,

Fedorov²

2014

Physics Letters A

View full text Add to dashboard Cite

We study a behavior of two-qubit states subject to tomographic measurement. In this Letter we propose a novel approach to definition of asymmetry in quantum bipartite state based on its tomographic Shannon entropies. We consider two types of measurement bases: the first is one that diagonalizes density matrices of subsystems and is used in a definition of tomographic discord, and the second is one that maximizes Shannon mutual information and relates to symmetrical form quantum discord. We show how these approaches relate to each other and then implement them to the different classes of two-qubit states. Consequently, new subclasses of X-states are revealed.

show abstract

“…It follows from the general group theoretical arguments that, making use of the unitary irreducible square integrable representation of the tomographic group under consideration, a unified tomographic prescription can be developed for both finite dimensional and continuous variable systems [328]. Tomograms for spin states have been developed as projections on an arbitrary axis [329] as well as by using a discrete variable analog of symplectic tomography [330]. Tomograms of optical systems have been well studied in the past [37,291,305,331,332].…”

Section: Introductionmentioning

confidence: 99%

A theoretical study of nonclassical effects in optical and spin systems and their applications

Thapliyal

2018

Preprint

View full text Add to dashboard Cite

LIST OF PUBLICATIONS DURING Ph.D. THESIS WORK 231viii PREFACE AND ACKNOWLEDGMENT two systems enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before."This may/may not be the most important feat in my life, but is certainly so far. Therefore, I would like to take this opportunity to thank everyone who had influenced my life and had played a significant role in it. To begin with, my grandfather, whose words, "I know you will make me proud", reverberate through my mind in my lamest moments to elate me.Today I feel that all my teachers, who lit my path allowing me to tread firmly through darkness, have their contributions in this work. I will thank especially my very first teacher, my sister Jyoti Di, for her patience during my initial inscriptions. I am also indebted to Dr. B.V. Tripathi and Dr. Hemwati Nandan for introducing me to the research field, which I feel has given me both peace of mind and reason of life.I am also grateful to all my bosom buddies Tarun, Pankaj, Shashi Bhushan, Pawan, and the one who is undergoing the same evolution as mine, Ravi, which helped both of us to vent out our frustrations. My roommates Rachit and Neeraj to endure a researcher roomie with an abnormal life and behavior for more than four years and still not to complain.Needless to say, my parents and family for the love and affection showered upon me, believing in me, and always understanding when I was not there for them.At the end, I will extend my gratitude to each and every person who shared his experiences to enlighten me in different phases of my life. Due to which I consider this my responsibility to dedicate the present piece of work to the light within all of us, part of which had emancipated me. May this work on light impart some light to light within us. I would also like to acknowledge the financial assistances I received in different phases of my research work from DST, JIIT, DRDO, and CSIR without which this work would not have been possible. TPSC for commending me as category A speaker, which provided me an opportunity to visit TPSC centers and present my work.

show abstract

Quaternion Representation and Symplectic Spin Tomography

Cited by 6 publications

References 28 publications

Quantum process in probability representation of quantum mechanics

Quantum process in probability representation of quantum mechanics

Tomographic causal analysis of two-qubit states and tomographic discord

A theoretical study of nonclassical effects in optical and spin systems and their applications

Contact Info

Product

Resources

About