scholarly journals DISTINGUISHING UNENTANGLED STATES WITH AN UNENTANGLED MEASUREMENT

2006 ◽  
Vol 04 (01) ◽  
pp. 219-232 ◽  
Author(s):  
WILLIAM K. WOOTTERS
Keyword(s):  
Tensor Product ◽  
Quantum States ◽  
Local Measurements ◽  
The Individual

In a 1991 paper, Asher Peres and the author theoretically analyzed a set of unentangled bipartite quantum states that could apparently be distinguished better by a global measurement than by any sequence of local measurements on the individual subsystems. The present paper returns to the same example, and shows that the best result so far achieved can alternatively be attained by a measurement that, while still global, is "unentangled" in the sense that the operator associated with each measurement outcome is a tensor product.

scholarly journals Quantum Information in Neural Systems

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 773
Author(s):  
Danko D. Georgiev
Keyword(s):  
Quantum Entanglement ◽  
Quantum Coherence ◽  
Quantum Physics ◽  
Quantitative Measure ◽  
Quantum States ◽  
Quantum Evolution ◽  
Einstein Relation ◽  
Schmidt Decomposition ◽  
The Central Nervous System ◽  
The Individual

Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck–Einstein relation between energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex.

Environmental and geographical effects on fog occurrence

2021 ◽  
Author(s):  
Iva Hunova ◽  
Marek Brabec ◽  
Marek Malý ◽  
Alexandru Dumitrescu ◽  
Jan Geletič
Keyword(s):  
Air Pollution ◽  
Environmental Factors ◽  
Tensor Product ◽  
Generalized Additive Models ◽  
Additive Models ◽  
Low Rank ◽  
Seasonal Component ◽  
Explanatory Variables ◽  
The Individual

<p>Fog is a very complex phenomenon (Gultepe et al., 2007). In some areas it can contribute substantially to hydrological and chemical inputs and is therefore of high environmental relevance (Blas et al., 2010). Fog formation is affected by numerous factors, such as meteorology, air pollution, terrain (geomorphology), and land-use.</p><p>In our earlier studies we addressed the role of meteorology and air pollution on fog occurrence (Hůnová et al., 2018) and long-term trends in fog occurrence in Central Europe (Hůnová et al., 2020). This study builds on earlier model identification of year-to-year and seasonal components in fog occurrence and brings an analysis of the deformation of the above components due to the individual explanatory variables. The aim of this study was to indicate the geographical and environmental factors affecting the fog occurrence.</p><p>       We have examined the data on fog occurrence from 56 meteorological stations of various types from Romania reflecting different environments and geographical areas. We used long-term records from the 1981–2017 period. </p><p>       We considered both the individual explanatory variables and their interactions. With respect to geographical factors, we accounted for the altitude and landform. With respect to environmental factors,   we accounted for proximity of large water bodies, and proximity of forests. Geographical data from Copernicus pan-European (e.g. CORINE land cover, high resolution layers) and local (e.g. Urban Atlas) projects were used. Elevation data from EU-DEM v1.1 were source for morphometric analysis (Copernicus, 2020).</p><p>        We applied a generalized additive model, GAM (Wood, 2017; Hastie & Tibshirani, 1990) to address nonlinear trend shapes in a formalized and unified way. In particular, we employed penalized spline approach with cross-validated penalty coefficient estimation. To explore possible deformations of annual and seasonal components with various covariates of interest, we used (penalized) tensor product splines to model (two-way) interactions parsimoniously, Wood (2006).</p><p>       The fog occurrence showed significant decrease over the period under review. In general the selected explanatory variables significantly affected the fog occurrence and their effect was non-linear. Our results indicated that, the geographical and environmental variables affected primarily the seasonal component of the model. Of the factors which were accounted for, it was mainly the altitude showing the clear effect on seasonal component deformation (Hůnová et al., in press).</p><p>      </p><p> </p><p>References:</p><p>Blas, M, Polkowska, Z., Sobik, M., et al. (2010). Atmos. Res. 95, 455–469.</p><p>Copernicus Land Monitoring Service (2020). Accessed online at: https://land.copernicus.eu/.</p><p>Gultepe, I., Tardif, R., Michaelidis, S.C., Cermak, J., Bott, A. et al. (2007). Pure Appl Geophys, 164, 1121-1159.</p><p>Hastie, T.J., Tibshirani, R.J. (1990). Generalized Additive Models. Boca Raton, Chapman & Hall/CRC.</p><p>Hůnová, I., Brabec, M., Malý, M., Dumitrescu, A., Geletič, J. (in press) Sci. Total Environ. 144359.</p><p>Hůnová, I., Brabec, M., Malý, M., Valeriánová, A. (2018) Sci. Total Environ. 636, 1490–1499.</p><p>Hůnová, I., Brabec, M., Malý, M., Valeriánová, A. (2020) Sci. Total Environ. 711, 135018.</p><p>Wood, S.N. (2006) Low rank scale invariant tensor product smooths for generalized additive mixed models. Biometrics 62(4):1025-1036</p><p>Wood, S.N. (2017). Generalized Additive Models: An Introduction with R (2nd ed). Boca Raton, Chapman & Hall/CRC.</p><p> </p>

The tensor product of supersymmetric N = (1,1) spectral data

2018 ◽  
Vol 15 (12) ◽  
pp. 1850207 ◽  
Author(s):  
Satyajit Guin
Keyword(s):  
Quantum Theory ◽  
Tensor Product ◽  
Spectral Data ◽  
Noncommutative Geometry ◽  
Product Formula ◽  
Unitary Connection ◽  
The Individual

We define the notion of tensor product of supersymmetric [Formula: see text] spectral data in the context of supersymmetric quantum theory and noncommutative geometry. We explain in which sense our definition is canonical and also establish its compatibility with the tensor product of [Formula: see text] spectral data defined earlier by Connes. As an application, we show that the unitary connections on the individual [Formula: see text] spectral data give rise to a unitary connection on the product [Formula: see text] spectral data.

scholarly journals Approximating Ground States by Neural Network Quantum States

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 82 ◽  
Author(s):  
Ying Yang ◽  
Chengyang Zhang ◽  
Huaixin Cao
Keyword(s):  
Neural Network ◽  
Tensor Product ◽  
Relative Error ◽  
Ground State ◽  
Ground States ◽  
Quantum States ◽  
The Neural Network

Motivated by the Carleo’s work (Science, 2017, 355: 602), we focus on finding the neural network quantum statesapproximation of the unknown ground state of a given Hamiltonian H in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.

scholarly journals Direct Measurement of Nonlinear Properties of Bipartite Quantum States

2006 ◽  
Vol 13 (03) ◽  
pp. 281-289
Author(s):  
F. A. Bovino ◽  
G. Castagnoli ◽  
A. Ekert ◽  
C. Moura Alves ◽  
P. Horodecki ◽  
...  
Keyword(s):  
Information Science ◽  
Quantum States ◽  
Full Description ◽  
Entangled Photons ◽  
Entanglement Witness ◽  
Entropic Inequalities ◽  
Nonlinear Properties ◽  
Local Measurements ◽  
Marking Technique ◽  
Chsh Inequalities

Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal and a nonlinear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with nondeterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a nonlinear entanglement witness and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities.

scholarly journals Locally restricted measurements on a multipartite quantum system: data hiding is generic

2015 ◽  
pp. 513-540
Author(s):  
Guillaume Aubrun ◽  
Cecilia Lancien
Keyword(s):  
Quantum System ◽  
Data Hiding ◽  
Quantum Measurements ◽  
Quantum States ◽  
Classical Communication ◽  
Substantial Loss ◽  
Local Measurements ◽  
System Data

We study the distinguishability norms associated to families of locally restricted POVMs on multipartite systems. These norms (introduced by Matthews, Wehner and Winter) quantify how quantum measurements, subject to locality constraints, perform in the task of discriminating two multipartite quantum states. We mainly address the following question regarding the behaviour of these distinguishability norms in the highdimensional regime: On a bipartite space, what are the relative strengths of standard classes of locally restricted measurements? We show that the class of PPT measurements typically performs almost as well as the class of all measurements whereas restricting to local measurements and classical communication, or even just to separable measurements, implies a substantial loss. We also provide examples of state pairs which can be perfectly distinguished by local measurements if (one-way) classical communication is allowed between the parties, but very poorly without it. Finally, we study how many POVMs are needed to distinguish almost perfectly any pair of states on C^d, showing that the answer is exp(Θ(d^2 )).

scholarly journals Obscure Qubits and Membership Amplitudes

2021 ◽  
Author(s):  
Steven Duplij ◽  
Raimund Vogl
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Density Matrix ◽  
Tensor Product ◽  
Quantum Computation ◽  
Membership Function ◽  
Quantum Probability ◽  
Quantum States ◽  
Born Rule ◽  
Quantum Amplitude

We propose a concept of quantum computing which incorporates an additional kind of uncertainty, i.e. vagueness (fuzziness), in a natural way by introducing new entities, obscure qudits (e.g. obscure qubits), which are characterized simultaneously by a quantum probability and by a membership function. To achieve this, a membership amplitude for quantum states is introduced alongside the quantum amplitude. The Born rule is used for the quantum probability only, while the membership function can be computed from the membership amplitudes according to a chosen model. Two different versions of this approach are given here: the “product” obscure qubit, where the resulting amplitude is a product of the quantum amplitude and the membership amplitude, and the “Kronecker” obscure qubit, where quantum and vagueness computations are to be performed independently (i.e. quantum computation alongside truth evaluation). The latter is called a double obscure-quantum computation. In this case, the measurement becomes mixed in the quantum and obscure amplitudes, while the density matrix is not idempotent. The obscure-quantum gates act not in the tensor product of spaces, but in the direct product of quantum Hilbert space and so called membership space which are of different natures and properties. The concept of double (obscure-quantum) entanglement is introduced, and vector and scalar concurrences are proposed, with some examples being given.

scholarly journals Device-independent certification of tensor products of quantum states using single-copy self-testing protocols

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 418
Author(s):  
Ivan Šupić ◽  
Daniel Cavalcanti ◽  
Joseph Bowles
Keyword(s):  
Tensor Product ◽  
Single Copy ◽  
Quantum States ◽  
High Dimensional ◽  
Entangled States ◽  
Testing Protocol ◽  
Self Testing ◽  
Rank One ◽  
Number Of Parties ◽  
Testing Protocols

Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.

Entanglement

Quantum 20/20 ◽  
2019 ◽  
pp. 151-162
Author(s):  
Ian R. Kenyon
Keyword(s):  
Quantum States ◽  
Entangled States ◽  
Entangled State ◽  
Entangled Photons ◽  
Photon State ◽  
Full Knowledge ◽  
Quantum Entangled States ◽  
The Individual ◽  
Down Conversion ◽  
Individual Particles

The distiction between classical product states and quantum entangled states is disclosed with examples. Spontaneous parametric down conversion as a source of entangled photons is described. The action of a perfect beam splitter is analysed using creation and annihilation operators. The HOM interferometer is described. Its use in demonstrating the indistinguishability of photons and in measuring bandwidth of sources at the level of femtoseconds is recounted. Two particle entanglement is analysed using the Bloch sphere representation showing how the full knowledge of the entangled state does not fix the state of the individual particles. The four Bell states, eigenstates of two particle entanglement, are introduced. Teleportation of a photon state using entangled photons is described, and an experiment to entangle the quantum states of atoms at space-like separation outlined.

MAXIMUM NONLOCAL EFFECTS OF QUANTUM STATES

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1587-1598 ◽  
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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