Data pattern tomography: reconstruction with an unknown apparatus

Mogilevtsev, D.; Ignatenko, Alexandr; Maloshtan, A. S.; Stoklasa, Bohumil; Řeháček, J.; Hradil, Z.

doi:10.1088/1367-2630/15/2/025038

Cited by 39 publications

(55 citation statements)

References 31 publications

(32 reference statements)

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“…From a practical point of view, it is essential to find optimal basis sets with the minimum possible number of coherent projectors for the representation. However, to our knowledge, the optimization of the basis choice has not yet been fully discussed and analyzed (here one can point to only two preliminary recent works [14,18]). In experiments [16,17] the reconstruction was done by considering only a set of probe states that was a priori deemed sufficiently large (from 48 to 150).…”

Section: Optimal Basis Setsmentioning

confidence: 99%

“…It is highly desirable to use the smallest possible number of basis states. If the observer believes that the signal state is very likely residing in some operator subspace, he or she can make use of this insight to define the set of probe states that spans this subspace for data-pattern reconstruction [13,14]. Naturally, the accuracy of the method depends crucially on the accuracy of the signal representation.…”

Section: Introductionmentioning

confidence: 99%

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Data-pattern tomography of entangled states

2017

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We discuss the data-pattern tomography for reconstruction of entangled states of light. We show that for a moderate number of probe coherent states it is possible to achieve high accuracy of representation not only for single-mode states but also for two-mode entangled states. We analyze the stability of these representations to the noise and demonstrate the conservation of the purity and entanglement. Simulating the probe and signal measurements, we show that systematic error inherent for representation of realistic signal response with finite sets of responses from probe states still allows one to infer reliably the signal states preserving entanglement.

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Section: Optimal Basis Setsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Data-pattern tomography of entangled states

2017

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“…[3] Any practice which takes into account SPAM errors will be generically referred to as SPAM tomography. Several works have come out in SPAM tomography [3][4][5][6][7][8][9][10] particular to the task of making estimates in spite of such conditions, all of which speak to the notion of a "self-consistent tomography." Of course, such works assume that any and all SPAM errors are uncorrelated.…”

Section: Introductionmentioning

confidence: 99%

Nonholonomic tomography. II. Detecting correlations in multiqudit systems

Jackson¹,

Enk²

2017

Phys. Rev. A

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In the context of quantum tomography, quantities called partial determinants [1] were recently introduced. PDs (partial determinants) are explicit functions of the collected data which are sensitive to the presence of state-preparation-and-measurement (SPAM) correlations. In this paper, we demonstrate further applications of the PD and its generalizations. In particular we construct methods for detecting various types of SPAM correlation in multiqudit systems -e.g. measurementmeasurement correlations. The relationship between the PDs of each method and the correlations they are sensitive to is topological. We give a complete classification scheme for all such methods but focus on the explicit details of only the most scalable methods, for which the number of settings scales as O(d 4 ). This paper is the second of a two part series where the first paper[2] is about a theoretical perspective for the PD, particularly its interpretation as a holonomy.

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“…Several works have come out to solve this, [3][4][5][6][7][8], all of which speak to the notion of a "self-consistent tomography." These works also make an important common assumption: that the uncontrolled fluctuations in the SPAM are not correlated.…”

Section: Introductionmentioning

confidence: 99%

Nonholonomic tomography. I. The Born rule as a connection between experiments

Jackson

Enk

2017

Phys. Rev. A

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In the context of quantum tomography, we recently introduced a quantity called a partial determinant [1]. PDs (partial determinants) are explicit functions of the collected data which are sensitive to the presence of state-preparation-and-measurment (SPAM) correlated errors. As such, PDs bypass the need to estimate state-preparation or measurement parameters individually. In the present work, we suggest a theoretical perspective for the PD. We show that the PD is a holonomy and that the notions of state, measurement, and tomography can be generalized to non-holonomic constraints. To illustrate and clarify these abstract concepts, direct analogies are made to parallel transport, thermodynamics, and gauge field theory. This paper is the first of a two part series where the second paper[2] is about scalable generalizations of the PD in multiqudit systems, with possible applications for debugging a quantum computer.

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Data pattern tomography: reconstruction with an unknown apparatus

Cited by 39 publications

References 31 publications

Data-pattern tomography of entangled states

Data-pattern tomography of entangled states

Nonholonomic tomography. II. Detecting correlations in multiqudit systems

Nonholonomic tomography. I. The Born rule as a connection between experiments

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