Quantifying precision loss in local quantum thermometry via diagonal discord

Sone, Akira; Zhuang, Quntao; Cappellaro, Paola

doi:10.1103/physreva.98.012115

Cited by 26 publications

(28 citation statements)

References 63 publications

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“…The exponentially diverging error is a consequence of the fact that for temperatures far below the lowest gap, the system is essentially in the ground state, irrespective of the exact value of T . Such an exponentially diverging error was found in various studies on low-temperature thermometry (see, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][19][20][21][22]). In particular, Eq.…”

Section: Context and Main Resultsmentioning

confidence: 53%

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Fundamental limits on low-temperature quantum thermometry with finite resolution

Potts

Brask

Brunner

2019

Quantum

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While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we develop a general approach to low-temperature quantum thermometry, taking into account restrictions arising not only from the sample but also from the measurement process. We derive a fundamental bound on the minimal uncertainty for any temperature measurement that has a finite resolution. A similar bound can be obtained from the third law of thermodynamics. Moreover, we identify a mechanism enabling sub-exponential scaling, even in the regime of finite resolution. We illustrate this effect in the case of thermometry on a fermionic tightbinding chain with access to only two lattice sites, where we find a quadratic divergence of the uncertainty. We also give illustrative examples of ideal quantum gases and a squarelattice Ising model, highlighting the role of phase transitions.

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Section: Context and Main Resultsmentioning

confidence: 53%

“…ponentially at low temperatures [6][7][8][9][10][11][12][13][14][15][16][17]. In fact, this exponential scaling can be derived from very general arguments [18][19][20][21], based on the energy spectra of the sample and the probe, and could therefore appear to represent a fundamental limit on thermometry.…”

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confidence: 99%

Fundamental limits on low-temperature quantum thermometry with finite resolution

Potts

Brask

Brunner

2019

Quantum

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“…3. However, we stress that, now that diagonal discord is shown to be a valid faithful measure as explained in the above sections, one should regard optimized discord and diagonal discord as the measures corresponding to two different ways of characterizing the quantum correlation, and which measure is preferable just depends on the physical or operational setting one is interested in (for instance, see [15,[20][21][22] for several scenarios in which diagonal discord plays the major role).…”

Section: Comparison With Optimized Quantum Discordmentioning

confidence: 99%

Diagonal quantum discord

Liu

Takagi

Lloyd

2019

J. Phys. A: Math. Theor.

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Quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement. This paper analyzes the properties of diagonal discord, a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices. In contrast to the optimized discord, diagonal discord is easily computable; it also finds connections to thermodynamics and resource theory. Here we further show that, for the generic case of non-degenerate local density matrices, diagonal discord exhibits desirable properties as a preferable discord measure. We employ the theory of resource destroying maps [Liu/Hu/Lloyd, PRL 118, 060502 (2017)] to prove that diagonal discord is monotonically nonincreasing under the operation of local discord nongenerating qudit channels, d > 2, and provide numerical evidence that such monotonicity holds for qubit channels as well. We also show that it is continuous, and derive a Fannes-like continuity bound. Our results hold for a variety of simple discord measures generalized from diagonal discord.

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“…This measure, which has been designated as quantum discord, is able to capture not only quantum correlations in entangled states but also in separable states [1]. The concept of quantum discord was initially introduced by Ollivier and Zurek [2], which is attracting increasing interest [3][4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Geometric Discord for Multi-qubit Systems

Zhu¹,

Hu²,

Li³

et al. 2021

Preprint

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Radhakrishnan et.al [Phys. Rev. Lett. 124, 110401 (2020)] proposed quantum discord to multipartite systems and derived explicit formulae for any states. These results are significant in capturing quantum correlations for multi-qubit systems. In this paper, we propose the geometric measure of multipartite quantum discord and obtain results for a large family of multi-qubit states. Intriguingly, our results demonstrate that for the family of states, multipartite geometric discord decreases exponentially as the number of parties increases while multipartite quantum discord not, therefore, we conclude that multipartite geometric discord could not reflect multipartite quantum discord in all cases. Furthermore, we investigated the dynamic behavior of geometric discord for the family of two-, three-and four-qubit states under phase noise acting on the first qubit. And we discover that sudden change of multipartite geometric discord can appear when phase noise act only on one part of the two-, three-and four-qubit states.

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Quantifying precision loss in local quantum thermometry via diagonal discord

Cited by 26 publications

References 63 publications

Fundamental limits on low-temperature quantum thermometry with finite resolution

Fundamental limits on low-temperature quantum thermometry with finite resolution

Diagonal quantum discord

Geometric Discord for Multi-qubit Systems

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