State-independent uncertainty relations from eigenvalue minimization

Giorda, Paolo; Maccone, Lorenzo; Riccardi, Alberto

doi:10.1103/physreva.99.052121

Cited by 17 publications

(15 citation statements)

References 38 publications

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“…(5b) for orthogonal observables, i.e., a • b = 0. An alternative approach studying uncertainty relations that give lower bounds to the sum of standard deviations was recently presented in [44].…”

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confidence: 99%

Experimental test of tight state-independent preparation uncertainty relations for qubits

et al. 2020

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The well-known Robertson-Schrödinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state dependence. Therefore, Abbott et al. introduced a general approach to derive tight state-independent uncertainty relations for qubit measurements [Mathematics 4, 8 (2016)]. The relations are expressed in two measures of uncertainty, which are standard deviation and entropy, both functions of the expectation value. Here, we present a neutron polarimetric test of the tight state-independent preparation uncertainty relations for orthogonal, as well as nonorthogonal, Pauli spin observables. The final results, obtained with pure and mixed spin states, reproduce the theoretical predictions clearly for arbitrary initial states of variable degree of polarization.

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Section: Fig 1 (A)mentioning

confidence: 99%

Experimental test of tight state-independent preparation uncertainty relations for qubits

et al. 2020

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“…Ever since its birth in 1927 [1], various uncertainty relations, as concrete realizations of the uncertainty principle, have been extensively and intensively studied. In particular, recently, the state-independent uncertainty relations have attracted a lot of attentions [2,3,4,5,6,7]. Whether deeper principles underlie quantum uncertainty and nonlocality has been listed as one of the challenging scientific problems on the occasion of celebrating the 125th anniversary of the academical journal Science [8].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty regions of observables and state-independent uncertainty relations

Zhang,

Luo,

Fei

et al. 2021

Preprint

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The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the tight uncertainty relations of variance or deviation via determining the uncertainty regions, which are formed by the tuples of two or more of quantum observables in random quantum states induced from the uniform Haar measure on the purified states. From the analytical formulae of these uncertainty regions, we present state-independent uncertainty inequalities satisfied by the sum of variances or deviations of two, three and arbitrary many observables, from which experimentally friend entanglement detection criteria are derived for bipartite and tripartite systems.

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“…Apart from their fundamental interest, uncertainty relations play a significant role in the field of quantum information processing, with several applications such as entanglement detection [7][8][9], quantum cryptography [10][11][12][13][14][15][16], quantum metrology [17] and foundational tests of quantum theory [18,19]. Motivated by their applicability, there has been an ongoing interest in reformulating uncertainty relations expressing trade-off of more than two incompatible observables, formalized in terms of variances [7,9,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], or via information entropies [35][36][37][38][39][40][41][42][43][44]. Recently several experimental tests have been carried out to verify different forms of uncertainty relations [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

Reena,

Karthik,

Tej

et al. 2021

Preprint

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We show that violation of variance based local sum uncertainty relation (LSUR) for angular momentum operators of a bipartite system, proposed by Hofmann and Takeuchi [Phys. Rev. A 68, 032103 (2003)], is necessary and sufficient for entanglement in two-qubit permutation symmetric state. Moreover, we also establish its one-to-one connection with negativity of covariance matrix [Phys. Lett. A 364, 203 (2007)] of the two-qubit reduced system of a permutation symmetric Nqubit state. Consequently, it is seen that the violation of the angular momentum LSUR serves as a necessary condition for pairwise entanglement in N -qubit system, obeying exchange symmetry. We illustrate physical examples of entangled permutation symmetric N -qubit systems, where violation of the local sum uncertainty relation manifests itself as a signature of pairwise entanglement.

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State-independent uncertainty relations from eigenvalue minimization

Cited by 17 publications

References 38 publications

Experimental test of tight state-independent preparation uncertainty relations for qubits

Experimental test of tight state-independent preparation uncertainty relations for qubits

Uncertainty regions of observables and state-independent uncertainty relations

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

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