Erratum: Quantifying spatial correlations of general quantum dynamics (2015 <i>New J. Phys</i>.<b> 17</b> 062001)

Rivas, Ana María Rivas; Müller, Markus

doi:10.1088/1367-2630/17/7/079602

Cited by 3 publications

(18 citation statements)

References 62 publications

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“…We have presented a lower bound for the measure for correlations of quantum dynamics proposed in Ref. [35]. We have shown how this lower bound can be evaluated without full knowledge of the quantum process and how it can be extended to multipartite systems.…”

Section: Discussionmentioning

confidence: 99%

“…In the following we review the correlation measure suggested in [35], which is based on the Choi-Jamio lkowski isomorphism [44,45], provid-ing a one-to-one mapping of the dynamics in a quantum system to a quantum state of a larger system. The mathematical construction underlying the isomorphism can be summarized as follows: consider a bipartite system S = S 1 ⊗ S 2 , as shown in Fig.…”

Section: Measure For Spatial Correlations In Quantum Dynamicsmentioning

confidence: 99%

“…3. The measure establishes a rigorous theoretical framework that allows for a definition and the study of maximally correlated dynamics and the properties that such dynamics need to fulfill [35]. Again, the concept of maximally correlated dynamics is analogous to the one of maximally entangled states in the resource theory of entanglement.…”

Section: Introductionmentioning

confidence: 99%

“…Whereas the proposed quantifier for dynamical correlations [35] allows one to study correlated dynamics in a variety of contexts, its general applicability comes at the price of requiring full knowledge of the quantum dynamics. Experimentally, this requires quantum process tomography of the full system which is only feasible in small-scale systems, and has been experimentally demonstrated for up to three qubits [43], and quickly becomes impractical for quantum systems of larger size.…”

Section: Introductionmentioning

confidence: 99%

“…The presented work is structured as follows: In Sec. 2 we introduce and review the correlation measure proposed in [35]. We present the derivation of a lower bound of the measure in Sec.…”

Section: Introductionmentioning

confidence: 99%

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Experimental quantification of spatial correlations in quantum dynamics

Postler

Rivas²,

Schindler

et al. 2018

Quantum

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Correlations between different partitions of quantum systems play a central role in a variety of many-body quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical correlations in the time evolution of multiple parts of a composite quantum system. A rigorous measure to quantify correlations in quantum dynamics based on a full tomographic reconstruction of the quantum process has been introduced recently [Á. Rivas et al., New Journal of Physics, 17(6) 062001 (2015).]. In this work, we derive a lower bound for this correlation measure, which does not require full knowledge of the quantum dynamics. Furthermore we also extend the correlation measure to multipartite systems. We directly apply the developed methods to a trapped ion quantum information processor to experimentally characterize the correlations in quantum dynamics for twoand four-qubit systems. The method proposed and demonstrated in this work is scalable, platform-independent and applicable to other composite quantum systems and quantum information processing architectures. We apply the method to estimate spatial correlations in environmental noise processes, which are crucial for the performance of quantum error correction procedures. * These authors contributed equally to this work.

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Section: Discussionmentioning

confidence: 99%

Section: Measure For Spatial Correlations In Quantum Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The presented work is structured as follows: In Sec. 2 we introduce and review the correlation measure proposed in [35]. We present the derivation of a lower bound of the measure in Sec.…”

Section: Introductionmentioning

confidence: 99%

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Experimental quantification of spatial correlations in quantum dynamics

Postler

Rivas²,

Schindler

et al. 2018

Quantum

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Bath‐Induced Collective Phenomena on Superconducting Qubits: Synchronization, Subradiance, and Entanglement Generation

et al. 2021

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A common environment acting on a pair of qubits gives rise to a plethora of different phenomena, such as the generation of qubit–qubit entanglement, quantum synchronization, and subradiance. Here, time‐independent figures of merit for entanglement generation, quantum synchronization, and subradiance are defined, and an extensive analytical and numerical study of their dependence on model parameters is performed. A recently proposed measure of the collectiveness of the dynamics driven by the bath is also addressed, and it is found that it almost perfectly witnesses the behavior of entanglement generation. The results show that synchronization and subradiance can be employed as reliable local signatures of an entangling common‐bath in a general scenario. Finally, an experimental implementation of the model based on two transmon qubits capacitively coupled to a common resistor is proposed, which provides a versatile quantum simulation platform of the open system in any regime.

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Relaxation times do not capture logical qubit dynamics

Pal

Schindler

Rivas³

et al. 2022

Quantum

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Quantum error correction procedures have the potential to enable faithful operation of large-scale quantum computers. They protect information from environmental decoherence by storing it in logical qubits, built from ensembles of entangled physical qubits according to suitably tailored quantum error correcting encodings. To date, no generally accepted framework to characterise the behaviour of logical qubits as quantum memories has been developed. In this work, we show that generalisations of well-established figures of merit of physical qubits, such as relaxation times, to logical qubits fail and do not capture dynamics of logical qubits. We experimentally illustrate that, in particular, spatial noise correlations can give rise to rich and counter-intuitive dynamical behavior of logical qubits. We show that a suitable set of observables, formed by code space population and logical operators within the code space, allows one to track and characterize the dynamical behaviour of logical qubits. Awareness of these effects and the efficient characterisation tools used in this work will help to guide and benchmark experimental implementations of logical qubits.

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Erratum: Quantifying spatial correlations of general quantum dynamics (2015 New J. Phys. 17 062001)

Cited by 3 publications

References 62 publications

Experimental quantification of spatial correlations in quantum dynamics

Experimental quantification of spatial correlations in quantum dynamics

Bath‐Induced Collective Phenomena on Superconducting Qubits: Synchronization, Subradiance, and Entanglement Generation

Relaxation times do not capture logical qubit dynamics

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