Optimal uncertainty relations in a modified Heisenberg algebra

Abdelkhalek, Kais; Chemissany, Wissam; Fiedler, Leander; Mangano, G.; Schwonnek, René

doi:10.1103/physrevd.94.123505

Cited by 19 publications

(18 citation statements)

References 84 publications

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“…The commutator we have studied is however well-motivated from the point of view of maintaining a UV momentum cut-off [27]. It can be associated with several variance-based uncertainty principles and for some measures of 'minimal length' can be expressed via entropic uncertainty relations as recently shown [65].…”

Section: Discussionmentioning

confidence: 99%

Testing generalised uncertainty principles through quantum noise

Girdhar

Doherty

2020

New J. Phys.

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Motivated by several approaches to quantum gravity, there is a considerable literature on generalised uncertainty principles particularly through modification of the canonical position–momentum commutation relations. Some of these modified relations are also consistent with general principles that may be supposed of any physical theory. Such modified commutators have significant observable consequences. Here we study the noisy behaviour of an optomechanical system assuming a certain commonly studied modified commutator. From recent observations of radiation pressure noise in tabletop optomechanical experiments as well as the position noise spectrum of advanced LIGO we derive bounds on the modified commutator. We find how such experiments can be adjusted to provide significant improvements in such bounds, potentially surpassing those from sub-atomic measurements.

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Section: Discussionmentioning

confidence: 99%

Testing generalised uncertainty principles through quantum noise

Girdhar

Doherty

2020

New J. Phys.

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“…4.1.1, we discuss their formulation in our setup. A related work [26] showed up too, which deals with the optimal bound for both variance and entropic uncertainty relations in the presence of minimal length. Compared to ours, their paper argues more detailed bound for the sum of entropy functions, but they use a special binning for p space (we take p as physical momentum and set up a natural binning for p).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Entropic uncertainty relation based on generalized uncertainty principle

2017

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We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

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“…This cost would eventually restrict the performance of a heat engine and a refrigerator. The cost for the projective measurement for one qubit is k B T ln 2 [52], which is the same as the cost of classical measurement of one bit. This leads to modified definition of the efficiency [53] as…”

Section: Effect Of Measurementmentioning

confidence: 70%

Measurement-induced operation of two-ion quantum heat machines

Chand

Biswas

2017

Phys. Rev. E

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We show how one can implement a quantum heat machine by using two interacting trapped ions, in presence of a thermal bath. The electronic states of the ions act like a working substance, while the vibrational mode is modelled as the cold bath. The heat exchange with the cold bath is mimicked by the projective measurement of the electronic states. We show how such measurement in a suitable basis can lead to either a quantum heat engine or a refrigerator, that undergoes a quantum Otto cycle. The local magnetic field is adiabatically changed during the heat cycle. The performance of the heat machine depends upon the interaction strength between the ions, the magnetic fields, and the measurement cost. In our model, the coupling to the hot and the cold baths are never switched off in an alternative fashion during the heat cycle, unlike other existing proposals of quantum heat engines. This makes our proposal experimentally realizable using current tapped-ion technology.

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Optimal uncertainty relations in a modified Heisenberg algebra

Cited by 19 publications

References 84 publications

Testing generalised uncertainty principles through quantum noise

Testing generalised uncertainty principles through quantum noise

Entropic uncertainty relation based on generalized uncertainty principle

Measurement-induced operation of two-ion quantum heat machines

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