Entangled quantum state discrimination using a pseudo-Hermitian system

Ghatak, Ananya; Mandal, Bhabani Prasad

doi:10.1088/1751-8113/45/35/355301

Cited by 11 publications

(10 citation statements)

References 40 publications

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“…This model has recently found an important application in quantum information theory where the positive definite metric operator constructed for this model plays a crucial role. The positive definite metric operator constructed for this model is extremely useful to discriminate two non-orthogonal entangled quantum states [17]. If a particular quantum system is described by two states, | ψ 1 and | ψ 2 which are non-orthogonal but differ very slightly, i.e.…”

Section: Pseudo-hermitian Scalar Interactionmentioning

confidence: 99%

“…Alternatively these non-orthogonal states are allowed to evolve with a pseudo-Hermitian Hamiltonian in the usual Hilbert space to become orthogonal at some later time. However such a time evolution is obstructed by the possible existence of exceptional points in the non-Hermitian system [17] .…”

Section: Pseudo-hermitian Scalar Interactionmentioning

confidence: 99%

“…The model of spin 1/2 particle which interacts with simple harmonic oscillator in a pseudo-Hermitian manner is shown to be useful to discriminate two entangled states of type [17],…”

Section: Application Of the Metric Operatorsmentioning

confidence: 99%

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Comparison of Different Approaches of Finding the Positive Definite Metric in Pseudo-Hermitian Theories

Ghatak¹,

Mandal²

2013

Commun. Theor. Phys.

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To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.

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Section: Pseudo-hermitian Scalar Interactionmentioning

confidence: 99%

Section: Pseudo-hermitian Scalar Interactionmentioning

confidence: 99%

See 1 more Smart Citation

Comparison of Different Approaches of Finding the Positive Definite Metric in Pseudo-Hermitian Theories

Ghatak¹,

Mandal²

2013

Commun. Theor. Phys.

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“…Many of the predictions of such theories have been verified experimentally in analogous classical systems [5]. These experimental realisations of non-Hermitian systems in laboratories prompted huge interests in the study of non-Hermitian systems both in theory and in experiments and rapidly developed over variousbranches of physics [6]. We are not attempting to account all important features of such theories in his brief note, rather present two of the major characteristics of these theories.…”

Section: Introductionmentioning

confidence: 99%

Some Aspects of Complex Quantum Theories: A Brief Note

Mandal¹

2019

J. Mountain Res.

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Theories with indefinite metric have a long and very rich history. Such theories are being used time to time in searching the solutions for many outstanding problems in physics over the several decades. However much attentions were not paid for these as they were not mathematically consistent with usual quantum theories. Towards the end of last century this field of research received huge boost, when attempts had been made to accommodate certain class of non-Hermitian theories in rigorous mathematical formulation. Subsequently it has been shown that certain specific types of non-Hermitian theories can lead to fully consistent quantum theories with complete real spectrum, unitary time evolution and probabilistic interpretation in a modified Hilbert space. Due to this important realisation, theories with complex Hamiltonian have become the topic of frontier research over last two decades and enormous applicationswere found in various branches of physics. In this brief note we try to review certain aspects of such theories where we have contributed. In particular, we discuss PT phase transitionin non-relativistic, relativistic and quantum field theoretic systems and some new features of scattering in complex systems.

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“…Certain class of non-Hermitian systems with real energy eigenvalues has become the topic of frontier research over a decade and half because one can have fully consistent quantum theory by restoring the Hermiticity and upholding the unitary time evolution for such system in a modified Hilbert space [1]- [3]. The study of non-Hermitian system has received a huge boost in this decade when some of the predictions of such theories were experimentally observed in optics [4]- [7] and therefore such theories have found many applications in different branches of physics [8]- [12]. Non-Hermitian theories have very rich scattering properties.…”

Section: Introductionmentioning

confidence: 99%

A black potential for spin less particles

2015

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We consider the most general non-Hermitian Hulthen potential to study the scattering of spin-less relativistic particles. The conditions for CC, SS and CPA are obtained analytically for this potential. We show that almost total absorption occurs for entire range of incidence energy for certain parameter ranges of the potential and hence term this as `black potential'. Time reversed of the same potential shows perfect emission for the entire range of particle energy. We also present the classical analog of this potential in terms of waveguide cross section.Comment: Latex, 23 pages, 7 Fig

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Entangled quantum state discrimination using a pseudo-Hermitian system

Cited by 11 publications

References 40 publications

Comparison of Different Approaches of Finding the Positive Definite Metric in Pseudo-Hermitian Theories

Comparison of Different Approaches of Finding the Positive Definite Metric in Pseudo-Hermitian Theories

Some Aspects of Complex Quantum Theories: A Brief Note

A black potential for spin less particles

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