Adaptive Quantum State Tomography Improves Accuracy Quadratically

Mahler, Dylan H.; Rozema, Lee A.; Darabi, Ardavan; Ferrie, Christopher; Blume-Kohout, Robin; Steinberg, Aephraim M.

doi:10.1103/physrevlett.111.183601

Cited by 137 publications

(186 citation statements)

References 28 publications

(38 reference statements)

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“…It has been found that the precision achieved by tomography methods after a fixed number of measurements is dependent on the unknown state or process. This has naturally led to adaptive schemes [17,18] in which dynamic measurement settings are used. However, regardless of the measurement scheme-adaptive or nonadaptive-the precision is always limited by the unavoidable statistical fluctuation, where the ultimate precision limits are dictated by quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Quantum-enhanced tomography of unitary processes

Zhou¹,

Cable²,

Whittaker³

et al. 2015

Optica

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This is the final published version of the article (version of record). It first appeared online via OSA at https://www.osapublishing.org/optica/abstract.cfm?uri=optica-2-6-510. Please refer to any applicable terms of use of the publisher. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. A fundamental task in photonics is to characterize an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Among many ways to achieve this, single-photon probes can be used in a method called quantum process tomography (QPT). However, the precision of QPT is limited by unavoidable shot noise when implemented using single-photon probes or laser light. In situations where measurement resources are limited, for example, where the process (sample) to be probed is very delicate such that the exposure to light has a detrimental effect on the sample, it becomes essential to overcome this precision limit.Here we devise a scheme for process tomography with a quantum-enhanced precision by drawing upon techniques from quantum metrology. We implement a proof-of-principle experiment to demonstrate this scheme-four-photon quantum states are used to probe an unknown arbitrary unitary process realized with an arbitrary polarization rotation. Our results show a substantial reduction of statistical fluctuations compared to traditional QPT methods-in the ideal case, one four-photon probe state yields the same amount of statistical information as twelve single probe photons.

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Section: Introductionmentioning

confidence: 99%

Quantum-enhanced tomography of unitary processes

Zhou¹,

Cable²,

Whittaker³

et al. 2015

Optica

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“…(4) in Ref. 13 . This implies that the treatment of the remaining copies of the unknown state ρ T as distributed uniformly in the measurement settings is not the best choice.…”

Section: Discussionmentioning

confidence: 99%

“…Since N · R copies of ρ T are consumed in the first round of measurements, the remaining copies of ρ T have the number N · (1 − R) which are used to reduce the error of each entry of the density matrix ρ E0 as much as possible. Since the error caused by an entry with large modulus is also big 13 , a large number of samples of ρ T are required to reduce the errors of these entries.…”

Section: Selection Scheme Of Settingmentioning

confidence: 99%

“…The first step is to get a preliminary density matrix and the second step is to correct it by measurements of the diagonal basis of the density matrix obtained previously 13 . It reduces the infidelity between the estimated and the true state from O(1/ √ N) to O(1/N), where N is the total number of samples of the unknown state 13 . This idea is further substantiated by one-qubit experiment 15 .…”

Section: Introductionmentioning

confidence: 99%

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Enhancing multi-step quantum state tomography by PhaseLift

Zhao

2017

Annals of Physics

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Multi-photon system has been studied by many groups, however the biggest challenge faced is the number of copies of an unknown state are limited and far from detecting quantum entanglement. The difficulty to prepare copies of the state is even more serious for the quantum state tomography. One possible way to solve this problem is to use adaptive quantum state tomography, which means to get a preliminary density matrix in the first step and revise it in the second step. In order to improve the performance of adaptive quantum state tomography, we develop a new distribution scheme of samples and extend it to three steps, that is to correct it once again based on the density matrix obtained in the traditional adaptive quantum state tomography.Our numerical results show that the mean square error of the reconstructed density matrix by our new method is improved to the level from 10 −4 to 10 −9 for several tested states. In addition, PhaseLift is also applied to reduce the required storage space of measurement operator.a) qzhaoyuping@bit.edu.cn

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“…It is known to be a complex task, however, under certain assumptions it can be efficiently applied also to large systems [6][7][8][9][10][11] and even the accuracy can be assessed [12][13][14][15]. QPT deals with a scenario when an experimenter is given an unknown input-output black box E. In each run of the experiment he prepares some test state ̺ and performs a measurement M , thus, he choses the setting x = (̺, M ), and, records the outcome E k , where E k ∈ M .…”

Section: Quantum Process Tomographymentioning

confidence: 99%

Process estimation in the presence of time-invariant memory effects

Rybár

Ziman

2015

Phys. Rev. A

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Any repeated use of a fixed experimental instrument is subject to memory effects. We design an estimation method uncovering the details of the underlying interaction between the system and the internal memory without having any experimental access to memory degrees of freedom. In such case, by definition, any memoryless quantum process tomography (QPT) fails, because the observed data sequences do not satisfy the elementary condition of statistical independence. However, we show that the randomness implemented in certain QPT schemes is sufficient to guarantee the emergence of observable "statistical" patterns containing complete information on the memory channels. We demonstrate the algorithm in details for case of qubit memory channels with two-dimensional memory. Interestingly, we found that for arbitrary estimation method the memory channels generated by controlled unitary interactions are indistinguishable from memoryless unitary channels.

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Adaptive Quantum State Tomography Improves Accuracy Quadratically

Abstract: General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available:

Cited by 137 publications

References 28 publications

Quantum-enhanced tomography of unitary processes

Quantum-enhanced tomography of unitary processes

Enhancing multi-step quantum state tomography by PhaseLift

Process estimation in the presence of time-invariant memory effects

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