Minimal scheme for certifying three-outcome qubit measurements in the
prepare-and-measure scenario
- URL: http://arxiv.org/abs/2105.09925v2
- Date: Wed, 12 Jan 2022 20:19:47 GMT
- Title: Minimal scheme for certifying three-outcome qubit measurements in the
prepare-and-measure scenario
- Authors: Jonathan Steinberg, H. Chau Nguyen, Matthias Kleinmann
- Abstract summary: The number of outcomes is a defining property of a quantum measurement.
The certification of this property is possible in a semi-device-independent way.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The number of outcomes is a defining property of a quantum measurement, in
particular, if the measurement cannot be decomposed into simpler measurements
with fewer outcomes. Importantly, the number of outcomes of a quantum
measurement can be irreducibly higher than the dimension of the system. The
certification of this property is possible in a semi-device-independent way
either based on a Bell-like scenario or by utilizing the simpler
prepare-and-measure scenario. Here we show that in the latter scenario the
minimal scheme for a certifying an irreducible three-outcome qubit measurement
requires three state preparations and only two measurements and we provide
experimentally feasible examples for this minimal certification scheme. We also
discuss the dimension assumption characteristic to the semi-device-independent
approach and to which extend it can be mitigated.
Related papers
- Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios [0.0]
Self-testing is a promising approach to certifying quantum states or measurements.
We show how to self-test any four- (three-) outcome extremal positive operator-valued measure using a linear witness.
One of our constructions achieves self-testing of any number of states with the help of as many projective measurements.
arXiv Detail & Related papers (2024-06-12T21:47:19Z) - Some Entanglement Survives Most Measurements [1.3812010983144802]
We investigate the limitations of repeated non-projective measurements in preparing a quantum system.
We show that some entanglement remains unless one of the measurement operators becomes perfectly projective.
We present results for $n$-qubit and $n$-dimensional input states.
arXiv Detail & Related papers (2023-02-14T08:02:27Z) - Self-testing composite measurements and bound entangled state in a
unified framework [0.0]
We introduce a single scheme allowing to certify three different types of composite projective measurements acting on a three-qubit Hilbert space.
We certify a basis exhibiting NLWE in the smallest dimension capable of supporting this phenomenon.
On the other hand, the possibility of certification of a measurement obtained from a UPB has an interesting implication.
arXiv Detail & Related papers (2023-01-26T20:50:20Z) - High-dimensional entanglement certification: bounding relative entropy
of entanglement in $2d+1$ experiment-friendly measurements [77.34726150561087]
Entanglement -- the coherent correlations between parties in a quantum system -- is well-understood and quantifiable.
Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging.
We present a novel certification method whose measurement requirements scale linearly with dimension subsystem.
arXiv Detail & Related papers (2022-10-19T16:52:21Z) - Experimentally determining the incompatibility of two qubit measurements [55.41644538483948]
We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements.
We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons' polarization degrees of freedom.
arXiv Detail & Related papers (2021-12-15T19:01:44Z) - Certification of incompatible measurements using quantum steering [0.0]
We consider the problem of certification of quantum measurements with an arbitrary number of outcomes.
We propose a simple scheme for certifying any set of $d$-outcome projective measurements which do not share any common invariant proper subspace.
arXiv Detail & Related papers (2021-07-01T13:04:47Z) - Sample-efficient device-independent quantum state verification and
certification [68.8204255655161]
Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing.
We develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime.
We show that device-independent verification can be performed with optimal sample efficiency.
arXiv Detail & Related papers (2021-05-12T17:48:04Z) - Self-testing of binary Pauli measurements requiring neither entanglement
nor any dimensional restriction [0.0]
We propose a self-testing protocol for certifying binary Pauli measurements employing the violation of a Leggett-Garg inequality.
Unlike previously proposed self-testing protocols in the prepare and measure scenario, our approach requires neither dimensional restrictions, nor other stringent assumptions on the type of measurements.
arXiv Detail & Related papers (2020-12-14T14:38:42Z) - On the optimal certification of von Neumann measurements [55.41644538483948]
certification of quantum measurements can be viewed as the extension of quantum hypotheses testing.
We show the connection between the certification of quantum channels or von Neumann measurements and the notion of $q$-numerical range.
arXiv Detail & Related papers (2020-09-14T22:38:23Z) - Quantum probes for universal gravity corrections [62.997667081978825]
We review the concept of minimum length and show how it induces a perturbative term appearing in the Hamiltonian of any quantum system.
We evaluate the Quantum Fisher Information in order to find the ultimate bounds to the precision of any estimation procedure.
Our results show that quantum probes are convenient resources, providing potential enhancement in precision.
arXiv Detail & Related papers (2020-02-13T19:35:07Z) - Distributed, partially collapsed MCMC for Bayesian Nonparametrics [68.5279360794418]
We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures.
We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components.
The resulting hybrid algorithm can be applied to allow scalable inference without sacrificing convergence guarantees.
arXiv Detail & Related papers (2020-01-15T23:10:13Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.