Unified entropic measures of quantum correlations induced by local measurements

2011 ◽

Vol 09 (supp01) ◽

pp. 165-179

Author(s):

FRANCISCO DELGADO

Keyword(s):

Magnetic Field ◽

Quantum Correlations ◽

Inhomogeneous Magnetic Field ◽

Original State ◽

Communication Processes ◽

Local Measurements ◽

Non Local ◽

And Behavior ◽

And Control ◽

Measurement And Control

Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume stable resources, not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. quantum computation or quantum cryptography). The presence of parasite magnetic fields modifies the expected properties and behavior for which the pair was intended. Quantum measurement and control help to discriminate the original state in order to correct it or reconstruct it using some procedures which do not alter their quantum nature. Different kinds of quantum entangled pairs driven by a Heisenberg Hamiltonian with an additional inhomogeneous magnetic field become distorted. They can be reconstructed by adding an external magnetic field with fidelity close to one. In addition, each state can be efficiently discriminated. Combining both processes, first reconstruction without discrimination and after discrimination with adequate non-local measurements, it is possible to (a) improve the discrimination, and (b) reprepare faithfully the original state. The complete process gives fidelities better than 0.9. Some results about a class of equivalence for the required measurements are found, allowing to select the experimentally most adequate.

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Bounding sets of sequential quantum correlations and device-independent randomness certification

Quantum ◽

10.22331/q-2020-10-19-344 ◽

2020 ◽

Vol 4 ◽

pp. 344 ◽

Cited By ~ 1

Author(s):

Joseph Bowles ◽

Flavio Baccari ◽

Alexia Salavrakos

Keyword(s):

Quantum Information ◽

Arbitrary Dimension ◽

Quantum Correlations ◽

Entangled State ◽

Outer Approximations ◽

Resource Requirements ◽

Local Measurements ◽

Local Randomness ◽

Test Scenarios ◽

Sequential Measurements

An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the NPA hierarchy; an infinite sequence of semidefinite programs that provides increasingly tighter outer approximations to the desired set of correlations. In this work we consider a more general scenario in which one performs sequences of local measurements on an entangled state of arbitrary dimension. We show that a simple adaptation of the original NPA hierarchy provides an analogous hierarchy for this scenario, with comparable resource requirements and convergence properties. We then use the method to tackle some problems in device-independent quantum information. First, we show how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements. Finally, we show tight upper bounds to two previously defined tasks in sequential Bell test scenarios.

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An artificial spiking quantum neuron

npj Quantum Information ◽

10.1038/s41534-021-00381-7 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Lasse Bjørn Kristensen ◽

Matthias Degroote ◽

Peter Wittek ◽

Alán Aspuru-Guzik ◽

Nikolaj T. Zinner

Keyword(s):

Time Series Prediction ◽

Dynamical Evolution ◽

Building Blocks ◽

Quantum Correlations ◽

Neuromorphic Hardware ◽

Local Measurements ◽

Non Local ◽

Elementary Building ◽

Learning Protocols

AbstractArtificial spiking neural networks have found applications in areas where the temporal nature of activation offers an advantage, such as time series prediction and signal processing. To improve their efficiency, spiking architectures often run on custom-designed neuromorphic hardware, but, despite their attractive properties, these implementations have been limited to digital systems. We describe an artificial quantum spiking neuron that relies on the dynamical evolution of two easy to implement Hamiltonians and subsequent local measurements. The architecture allows exploiting complex amplitudes and back-action from measurements to influence the input. This approach to learning protocols is advantageous in the case where the input and output of the system are both quantum states. We demonstrate this through the classification of Bell pairs which can be seen as a certification protocol. Stacking the introduced elementary building blocks into larger networks combines the spatiotemporal features of a spiking neural network with the non-local quantum correlations across the graph.

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MAXIMUM NONLOCAL EFFECTS OF QUANTUM STATES

International Journal of Quantum Information ◽

10.1142/s0219749911008337 ◽

2011 ◽

Vol 09 (07n08) ◽

pp. 1587-1598 ◽

Cited By ~ 6

Author(s):

SHUANGSHUANG FU ◽

SHUNLONG LUO

Keyword(s):

Quantum Correlations ◽

Quantum Measurements ◽

Quantum States ◽

Nonlocal Effect ◽

Nonlocal Effects ◽

Bipartite State ◽

Local Quantum ◽

Local Measurements ◽

Minimum Disturbance ◽

Global And Local

A fundamental feature of quantum mechanics radically different from classical theory lies in the role and consequence of quantum measurements, which usually cause disturbance to quantum states. For a bipartite state, the minimum disturbance caused by local measurements has been used to define quantum correlations from a measurement perspective. In contrast to this minimum approach, we investigate the maximum disturbance of local measurements, and define the nonlocal effect of a bipartite state as the maximum discrepancy between the global and local disturbances caused by local quantum measurements. Some analytical results are obtained and the significance of the maximum nonlocal effect is briefly discussed.

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