Experimental test of uncertainty relations for general unitary operators

Liu, Xiao; Wang, Kunkun; Zhan, Xiang; Bian, Zhihao; Li, Jian; Zhang, Yongsheng; Xue, Peng; Pati, Arun Kumar

doi:10.1364/oe.25.017904

Cited by 30 publications

(23 citation statements)

References 33 publications

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“…(1) was improved by Schrödinger [5]. Recently, variancebased uncertainty relations have been intensely studied in [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Because of their relevance in quantum information theory, the entropies [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] have been employed to quantify the uncertainty relations between incompatible observables.…”

Section: Introductionmentioning

confidence: 99%

Strong unitary uncertainty relations

Jing

Li‐Jost

2019

Phys. Rev. A

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In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the well-known Cauchy-Schwarz inequality, our framework naturally improves the results based on the latter. As such, the unitary uncertainty relations based on our method outperform the best known bound introduced in [Phys. Rev. Lett. 120, 230402 (2018)] to some extent. Explicit examples of unitary uncertainty relations are provided to back our claims. arXiv:1908.05053v1 [quant-ph]

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Section: Introductionmentioning

confidence: 99%

Strong unitary uncertainty relations

Jing

Li‐Jost

2019

Phys. Rev. A

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“…The Heisenberg uncertainty principle—being related to precision of simultaneous measurements for a pair of noncommutative observables—is a foundational feature and fundamental insight of quantum theory . A later generalization was developed by Kennard and Robertson into a standard deviation

Δ S Δ R \geq | ⟨ [S, R] ⟩ | / 2

for a pair of arbitrary incompatible observables

scriptS

and

scriptR

. Notably, the standard deviation is not optimal for the quantification of the uncertainty because the lower bound is state dependent.…”

Section: Introductionmentioning

confidence: 99%

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

et al. 2018

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The Heisenberg uncertainty principle describes a basic restriction on an observer's ability of precisely predicting the measurement of a pair of noncommuting observables, and virtually is at the core of quantum mechanics. Herein, the aim is to study the entropic uncertainty relation (EUR) under the background of a Schwarzschild black hole and its control. Explicitly, dynamical features of the measuring uncertainty via entropy are developed in a practical model where a stationary particle interacts with its surrounding environment while another particle-serving as a quantum memory reservoir-undergoes free fall in the vicinity of the event horizon of the Schwarzschild space-time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive of the fact the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a genuine scenario is provided. Finally, an efficient strategy is proposed to reduce the uncertainty by non-tracing-preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space-time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.

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“…. U n and polarisation state ρ, and hence the testing of the UUR for any n. We note that, in comparison, a recent qutrit experiment testing a special case of the n = 2 UUR requires preparation of a strictly pure state |ψ , prior knowledge of the unitary operators (to implement both V and V † ), and tomographic reconstruction of |ψ , U |ψ and V |ψ [35].…”

mentioning

confidence: 99%

Strong Unitary and Overlap Uncertainty Relations: Theory and Experiment

et al. 2018

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We derive and experimentally investigate a strong uncertainty relation valid for any n unitary operators, which implies the standard uncertainty relation and others as special cases, and which can be written in terms of geometric phases. It is saturated by every pure state of any n-dimensional quantum system, generates a tight overlap uncertainty relation for the transition probabilities of any n+1 pure states, and gives an upper bound for the out-of-time-order correlation function. We test these uncertainty relations experimentally for photonic polarization qubits, including the minimum uncertainty states of the overlap uncertainty relation, via interferometric measurements of generalized geometric phases.

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Experimental test of uncertainty relations for general unitary operators

Cited by 30 publications

References 33 publications

Strong unitary uncertainty relations

Strong unitary uncertainty relations

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

Strong Unitary and Overlap Uncertainty Relations: Theory and Experiment

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