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

Jackson, Christopher; Enk, Steven van

doi:10.1103/physreva.95.052327

Cited by 6 publications

(7 citation statements)

References 16 publications

(34 reference statements)

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“…One last form of quantum tomography is state-preparation-and-measurement (SPAM) tomography [21][22][23][24][25]. SPAM tomography attempts to estimate both the state and measurement parameters in a self-consistent manner.…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of loop state-preparation-and-measurement tomography

2017

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We have performed an experiment demonstrating that loop state-preparation-and-measurement (SPAM) tomography [C. Jackson and S. J. van Enk, Phys. Rev. A 92, 042312 (2015)] is capable of detecting correlated errors between the preparation and the measurement of a quantum system. Specifically, we have prepared pure and mixed states of single qubits encoded in the polarization of heralded individual photons. By performing measurements using multiple state preparations and multiple measurement device settings we are able to detect if there are any correlated errors between them, and are also able to determine which state preparations are correlated with which measurements. This is accomplished by going around a "loop" in parameter space, which allows us to check for self-consistency. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positiveoperator-valued measures (POVMs) describing the detector are known. In cases where no correlations are found we are able to perform quantum state tomography of the polarization qubits by using knowledge of the detector POVMs, or quantum detector tomography by using knowledge of the state preparations. Note, however, that the detection of correlated errors does not require estimating any state or measurement parameters.Another form of tomography is quantum-detector tomography (QDT), which estimates the positive-operator-valued measure (POVM) that describes a detector [8][9][10][11][12]. Here the detector is illuminated with many different probe states, and the detector is characterized by measuring its response to these states. In QDT it is assumed that the states are known and well-characterized, but the detector POVM is initially unknown.In quantum-process tomography (QPT) the process that transforms an open quantum system from one state to another is fully characterized [13][14][15][16][17]. This is done by having known input states and performing QST on the output states.

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Section: Introductionmentioning

confidence: 99%

Experimental demonstration of loop state-preparation-and-measurement tomography

2017

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“…2 (a)-(b). We find that ( ) 2 Tr 0.866 ρ = ; this is a measure of the purity of the state. We then fit our measured ρ These parameters indicate that our source produces a state that is well described by Eq.…”

Section: No Background Illuminationmentioning

confidence: 84%

“…It is called the partial determinant because it is mathematically similar to the determinant, but it is not a scalar quantity-it is a matrix of smaller size than E . It can be shown that the measured data are internally consistent as described above, and free of correlated SPAM errors, if and only if ( ) 1 E D = , where 1 is the 3x3 identity matrix [1][2][3][4]. No knowledge of the state ρ or the detector operators is necessary to make this determination.…”

Section: A Loop Spam Tomographymentioning

confidence: 89%

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Loop state-preparation-and-measurement tomography of a two-qubit system

et al. 2018

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We experimentally demonstrate that loop state-preparation-and-measurement (SPAM) tomography is capable of detecting correlated errors in a two-qubit system. We prepare photon pairs in a state that approximates a Werner state, which may or may not be entangled. By performing measurements with multiple different detector settings we are able to detect correlated errors between two single-qubit measurements performed in different locations. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures describing the detectors are known. The only other needed information is experimentally measured expectation values, which are analyzed for self-consistency. This demonstrates that loop SPAM tomography is a useful technique for detecting errors that would degrade the performance of multiple-qubit quantum information processors.OCIS codes: (270.5585) Quantum information and processing; (270.0270) Quantum optics

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“…. Moreover, this example illustrates that noise can be artificially reassigned to different objects, as the state in equation (2) is closer to pure than the one in equation (9). Note that the range of gauge transformations is constrained by ò 2 and so cannot significantly change the effective temperature for systems with high quality readout.…”

Section: Assigning Errors To Operationsmentioning

confidence: 93%

On the freedom in representing quantum operations

et al. 2019

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We discuss the effects of a gauge freedom in representing quantum information processing devices, and its implications for characterizing these devices. We demonstrate with experimentally relevant examples that there exists equally valid descriptions of the same experiment which distribute errors differently among objects in a gate-set, leading to different error rates. Consequently, it can be misleading to attach a concrete operational meaning to figures of merit for individual gate-set elements. We propose an alternative operational figure of merit for a gate-set, the mean variation error, and a protocol for measuring this figure.

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

Cited by 6 publications

References 16 publications

Experimental demonstration of loop state-preparation-and-measurement tomography

Experimental demonstration of loop state-preparation-and-measurement tomography

Loop state-preparation-and-measurement tomography of a two-qubit system

On the freedom in representing quantum operations

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