Nonclassicality in phase-number uncertainty relations

Matía-Hernando, Paloma; Luis, Alfredo

doi:10.1103/physreva.84.063829

Cited by 6 publications

(7 citation statements)

References 33 publications

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“…Moreover, since Theorem 1 involves operators of the form e iλ Ô it becomes valuable when the operator Ô does not exist itself (consequences of so called Stone-von Neumann theorem). A particularly interesting example of the number-phase uncertainty [58][59][60] (phase operators are not well defined) has just been described [61] along the lines of Theorem 1. Here we would like to briefly touch upon the broad theory of Loop Quantum Gravity [73], in which the so called Ashtekar connection [62] A i a (x) [74] plays the role of the canonical "position" variable in a field-theoretical sense [75].…”

Section: Proof Let Us Now Outline the Proof Of Theoremmentioning

confidence: 99%

Uncertainty relations for characteristic functions

Rudnicki¹,

Tasca²,

Walborn³

2016

Phys. Rev. A

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We present the uncertainty relation for the characteristic functions (ChUR) of the quantum mechanical position and momentum probability distributions. This inequality is more general than the Heisenberg Uncertainty Relation, and is saturated in two extremal cases for wavefunctions described by periodic Dirac combs. We further discuss a broad spectrum of applications of the ChUR, in particular, we constrain quantum optical measurements involving general detection apertures and provide the uncertainty relation that is relevant for Loop Quantum Cosmology. A method to measure the characteristic function directly using an auxiliary qubit is also briefly discussed

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Section: Proof Let Us Now Outline the Proof Of Theoremmentioning

confidence: 99%

Uncertainty relations for characteristic functions

Rudnicki¹,

Tasca²,

Walborn³

2016

Phys. Rev. A

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“…[11] is a quite interesting formulation particularly suited to phase-angle variables. We also show that this encounters fundamental ambiguities when contrasting different slightly different alternative implementations, as it also holds for other approaches [12][13][14].…”

Section: Introductionmentioning

confidence: 56%

“…(12) we get that the minimum uncertainty states are those pure states with s y = 0 and |s x | = |s z | = 1/ √ 2. On the other hand, the states with s y = 0 and |s x | = 0 or |s z | = 0 are of maximum uncertainty, contrary to the predictions of the sum relations (10) and (13).…”

Section: A Example: Qubitmentioning

confidence: 64%

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Phase–number uncertainty from Weyl commutation relations

Luis

Donoso

2017

Annals of Physics

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We derive suitable uncertainty relations for characteristics functions of phase and number variables obtained from the Weyl form of commutation relations. This is applied to finite-dimensional spinlike systems, which is the case when describing the phase difference between two field modes, as well as to the phase and number of a single-mode field. Some contradictions between the product and sums of characteristic functions are noted.

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“…In addition, a scheme has been suggested for preparation of superposed state (1) in a cavity [27]. Therefore, because of the fact that the construction of various classes of nonclassical states [28][29][30], as well as (and more importantly) their theoretical generation [31][32][33][34][35][36][37][38][39], are still of great interest for research in quantum optics field, in this paper we motivate to propose a method to generate a few classes of nonclassical states.…”

Section: Introductionmentioning

confidence: 99%

On the generation of number states, their single- and two-mode superpositions, and two-mode binomial state in a cavity

2014

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The proposed schemes in this paper involve the interaction of a two-level atom with single-or two-mode quantized cavity fields (for different purposes) in the presence of a classical field. Indeed, following the path of Solano et al. in [Phys. Rev. Lett. 90, 027903 (2003)], the behavior of the entire atom-field system may be described by the Jaynes-Cummings (JC)-and anti-Jaynes-Cummings (anti-JC)-like models. It is illustrated that, under specific conditions, the effective Hamiltonian of the system can be switched from a JC-to an anti-JC-like model. During the process, the two-level atom in the cavity is alternately affected by the above two effective interactions. Ultimately, after the occurrence of the desired interactions in appropriate setups, the cavity field will arrive at a specific superposition of number states, a fixed number state, and in particular, two-mode binomial field states. Moreover, the entanglement property of the two-mode binomial state is investigated by evaluating the entropy criterion. While there exist various proposals for preparation of number states and their superpositions in the literature, our scheme has the advantage that it is independent of the detection of the atomic state after the interaction occurs.

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Nonclassicality in phase-number uncertainty relations

Cited by 6 publications

References 33 publications

Uncertainty relations for characteristic functions

Uncertainty relations for characteristic functions

Phase–number uncertainty from Weyl commutation relations

On the generation of number states, their single- and two-mode superpositions, and two-mode binomial state in a cavity

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