Device-independent tests of quantum channels

Dall’Arno, Michele; Brandsen, Sarah; Buscemi, Francesco

doi:10.1098/rspa.2016.0721

Cited by 26 publications

(54 citation statements)

References 33 publications

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“…The schemes using Bell inequalities cannot be used with a single qutrit and moreover, recently it turned out that their violation can also be observed with pairs of qubit systems [23,24]. The approach in [19], based on a result on noiseless n-level quantum channels [25], is, however, restricted to some specific channels, which are inserted between the preparation and the measurement. In [20], the results are not limited to specific measurement, but they are restricted to the qubit case.…”

Section: Dimension Witnessesmentioning

confidence: 99%

“…For this, let us define the vector where we used the fact that due to observation 1, we can factorize the probabilities ( | ) p ab xy into the conditional probabilities ( | ) p a x and ( | ) p b axy . If we replace the probabilities ( | ) p a x and ( | ) p b axy with the respective coefficients in the vectors in equations (19) and (20), we obtain which is still a convex combination of deterministic assignments. Since we can construct vectors like this for every choice of x and y, we find that all non-deterministic assignments for the vector v are convex combinations of deterministic assignments.…”

Section: Appendix a Proof Of The Observations 1 Andmentioning

confidence: 99%

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Structure of temporal correlations of a qubit

et al. 2018

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In quantum mechanics, spatial correlations arising from measurements at separated particles are well studied. This is not the case, however, for the temporal correlations arising from a single quantum system subjected to a sequence of generalized measurements. We first characterize the polytope of temporal quantum correlations coming from the most general measurements. We then show that if the dimension of the quantum system is bounded, only a subset of the most general correlations can be realized and identify the correlations in the simplest scenario that can not be reached by twodimensional systems. This leads to a temporal inequality for a dimension test, and we discuss a possible implementation using nitrogen-vacancy centers in diamond.

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Section: Dimension Witnessesmentioning

confidence: 99%

Section: Appendix a Proof Of The Observations 1 Andmentioning

confidence: 99%

Structure of temporal correlations of a qubit

et al. 2018

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“…For some given observed correlation { } | p j i , conventional tomography provides a protocol to reconstruct the channel  T that best fits the black-box circuit ð1Þ From the above, it is clear that, while the inner channel is unknown, the probing preparation {ρ i } and the final measurement {π j } are completely known: in particular, they must satisfy a condition of linear completeness usually referred to as informational completeness.In order to move towards a DD approach, we first need to consider a situation somewhat complementary to that of conventional tomography. This is done by introducing the set   ( ) of correlations compatible with a given channel , as follows [11] ð2Þ where each distribution { } | p j i in the set is obtained by varying the input preparation {ρ i } and the final measurement {π j } (which are hence represented by the wildcard ' * '). The ability to characterize   ( ) with respect to any given prior information, that is for all channels in a given set  of possible channels, is the necessary prerequisite to perform DD inference within set .Before turning our attention to DD inference, let us remark that equations (1) and(2) suggest a very simple criterion to corroborate [28], in a fully DD fashion, the reconstruction obtained through conventional tomography:…”

mentioning

confidence: 99%

“…In order to move towards a DD approach, we first need to consider a situation somewhat complementary to that of conventional tomography. This is done by introducing the set   ( ) of correlations compatible with a given channel , as follows [11] ð2Þ where each distribution { } | p j i in the set is obtained by varying the input preparation {ρ i } and the final measurement {π j } (which are hence represented by the wildcard ' * '). The ability to characterize   ( ) with respect to any given prior information, that is for all channels in a given set  of possible channels, is the necessary prerequisite to perform DD inference within set .…”

mentioning

confidence: 99%

Data-driven inference of physical devices: theory and implementation

Buscemi

Dall’Arno

2019

New J. Phys.

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Given a physical device as a black box, one can in principle fully reconstruct its input-output transfer function by repeatedly feeding different input probes through the device and performing different measurements on the corresponding outputs. However, for such a complete tomographic reconstruction to work, full knowledge of both input probes and output measurements is required. Such an assumption is not only experimentally demanding, but also logically questionable, as it produces a circular argument in which the characterization of unknown devices appears to require other devices to have been already characterized beforehand. Here, we introduce a method to overcome such limitations present in usual tomographic techniques. We show that, even without any knowledge about the tomographic apparatus, it is still possible to infer the unknown device to a high degree of precision, solely relying on the observed data. This is achieved by employing a criterion that singles out the minimal explanation compatible with the observed data. Our method, that can be seen as a data-driven analog of tomography, is solved analytically and implemented as an algorithm for the learning of qubit channels.Quantum process tomography [1-9] is the standard protocol employed to reconstruct an unknown physical device, regarded as a black box. In a tomographic reconstruction, probes are repeatedly fed as inputs to the black box and measured at the output. The input-output transfer function of the black box can be reconstructed based on the correlations observed between the probes' preparations and the outcomes recorded in the final measurements. Such a reconstruction is reliable, however, only under the assumption that the entire tomographic procedure, comprising the probes' preparations and the final measurements, is fully known and trusted. Such an assumption, beside being quite demanding to fulfill in practice, is also unsatisfactory from a fundamental viewpoint, because it suggests that the knowledge required to implement tomography can only be obtained by recursively resorting to another tomographic reconstruction, and so on, ad infinitum.Here, we propose to solve such an impasse by adopting a data-driven (DD) approach [10-14] to data analysis in physical experiments. Such an approach relaxes any specific assumption about the devices involved in the experiment, in the sense that it does not require any knowledge of the input probes' preparations, nor of the final measurement settings (measurements for short). We then want to infer the unknown device only on the basis of the correlations observed in the data, without any assumption on the apparatus that was used to produce them, and with respect to any prior information that may (or may not) be already known about the device. We refer to such a task as DD inference of a physical device.However, the inference which explains the observed correlations is, generally speaking, not unique: clearly, the same set of observed correlations can be explained in many different ways, and each possibl...

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“…that of communication cost, has been explored in relation to both Bell nonlocality [24,25] and temporal correlations [26,27]. Similar notions have been explored also in the prepare-and-measure scenario [28][29][30][31][32] and in connection with quantum information tasks such as random access codes [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Memory cost of temporal correlations

2019

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A possible notion of nonclassicality for single systems can be defined on the basis of the notion of memory cost of classically simulating probabilities observed in a temporal sequence of measurements. We further explore this idea in a theory-independent framework, namely, from the perspective of general probability theories (GPTs), which includes classical and quantum theory as special examples. Under the assumption that each system has a finite memory capacity, identified with the maximal number of states perfectly distinguishable with a single measurement, we investigate what are the temporal correlations achievable with different theories, namely, classical, quantum, and GPTs beyond quantum mechanics. Already for the simplest nontrivial scenario, we derive inequalities able to distinguish temporal correlations where the underlying system is classical, quantum, or more general.

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Device-independent tests of quantum channels

Cited by 26 publications

References 33 publications

Structure of temporal correlations of a qubit

Structure of temporal correlations of a qubit

Data-driven inference of physical devices: theory and implementation

Memory cost of temporal correlations

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