Uncertainty Relation: From Inequality to Equality

1997 ◽  
Vol 52 (1-2) ◽  
pp. 49-52 ◽  
Author(s):  
Georg Süssmann
Keyword(s):  
Phase Space ◽  
Quantum State ◽  
Uncertainty Relation ◽  
The Other ◽  
Mixed States ◽  
Von Neumann ◽  
Other Hand ◽  
Pure Quantum State ◽  
Minimum Uncertainty

Abstract The uncertainty area δ (p, q): - [∫ W(p, q)2 dp dq] - 1 is proposed in place of δ p • δ q, and it is shown that each pure quantum state is a minimum uncertainty state in this sense: δ (p, q) = 2 π ħ. For mixed states, on the other hand, δ(p, q) > 2π ħ. In a phase space of 2F(=6N) dimensions, S: = k B • log[δF (p,q)/(2 π ħ)F] whit δF (p,q):= [∫ W(p, q)2 dF p dF q]-1 is considered as an alternative to von Neumann`s entropy S̃:= kB • trc [ρ̂ log (ρ̂-1)].

scholarly journals A Lightweight BCH Code Corrector of TRNG with Measurable Dependence

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Hojoong Park ◽  
Yongjin Yeom ◽  
Ju-Sung Kang
Keyword(s):  
Linear Code ◽  
Random Number ◽  
Random Number Generator ◽  
The Other ◽  
Bch Code ◽  
Compression Rate ◽  
Number Generator ◽  
Von Neumann ◽  
Other Hand ◽  
Cryptographic Algorithms

We propose a new lightweight BCH code corrector of the random number generator such that the bitwise dependence of the output value is controllable. The proposed corrector is applicable to a lightweight environment and the degree of dependence among the output bits of the corrector is adjustable depending on the bias of the input bits. Hitherto, most correctors using a linear code are studied on the direction of reducing the bias among the output bits, where the biased input bits are independent. On the other hand, the output bits of a linear code corrector are inherently not independent even though the input bits are independent. However, there are no results dealing with the independence of the output bits. The well-known von Neumann corrector has an inefficient compression rate and the length of output bits is nondeterministic. Since the heavy cryptographic algorithms are used in the NIST’s conditioning component to reduce the bias of input bits, it is not appropriate in a lightweight environment. Thus we have concentrated on the linear code corrector and obtained the lightweight BCH code corrector with measurable dependence among the output bits as well as the bias. Moreover, we provide some simulations to examine our results.

scholarly journals When is a dynamical system mean sensitive?

2017 ◽  
Vol 39 (06) ◽  
pp. 1608-1636 ◽  
Author(s):  
FELIPE GARCÍA-RAMOS ◽  
JIE LI ◽  
RUIFENG ZHANG
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
The Other ◽  
Positive Entropy ◽  
Topological Dynamical System ◽  
Other Hand ◽  
Open Question ◽  
Uniquely Ergodic ◽  
Mean Sensitivity ◽  
Transitive System

This article is devoted to studying which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things, we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive. On the other hand, we provide an example of a transitive system which is cofinitely sensitive or Devaney chaotic with positive entropy but fails to be mean sensitive. As applications of our theory and examples, we negatively answer an open question regarding equicontinuity/sensitivity dichotomies raised by Tu, we introduce and present results of locally mean equicontinuous systems and we show that mean sensitivity of the induced hyperspace does not imply that of the phase space.

scholarly journals Analysis of the affine transformations of the time-frequency plane

2001 ◽  
Vol 63 (2) ◽  
pp. 195-218 ◽  
Author(s):  
Filippo De Mari ◽  
Krzysztof Nowak
Keyword(s):  
Von Neumann Algebras ◽  
The Other ◽  
Affine Transformations ◽  
Metaplectic Representation ◽  
Von Neumann ◽  
Weyl Calculus ◽  
Time Frequency ◽  
Other Hand ◽  
The One

We consider two aspects of the action of the extended metaplectic representation of the groupGof affine, measure and orientation preserving maps of the time-frequency plane onL2functions on the line. On the one hand, we list, up to equivalence, all possible reproducing formulas that arise by restricting the representation to connected Lie subgroups ofG.On the other hand, we describe, in terms of Weyl calculus, the commutative von Neumann algebras generated by restriction to one-parameter subgroups.

Science with the Australia Telescope (Invited Paper)

1987 ◽  
Vol 7 (2) ◽  
pp. 220-226 ◽  
Author(s):  
B. J. Robinson
Keyword(s):  
Phase Space ◽  
Real Time ◽  
The Other ◽  
The Real ◽  
New Science ◽  
Long Baseline ◽  
Other Hand ◽  
Selection Of ◽  
Compact Array

AbstractThe research now under way with the real-time 275 km Parkes-Tidbinbila interferometer is used as a guide to the initial science to be undertaken with the 319 km Australia Telescope (AT) Long Baseline Array. On the other hand, it is risky to guess at the new science likely to be attempted with the 6 km AT Compact Array at Culgoora; instead the potential that has been built into this array is discussed and a selection of basic questions in astrophysics is posed as a guide to significant science that might yield to new observers on a fresh instrument under the southern skies. In conclusion two questions are probed: Can discoveries be made by users of national facilities? Does the AT cross into new domains in the phase space of observations?

Neurosis and Psychosis: An Experimental Analysis

1956 ◽  
Vol 102 (428) ◽  
pp. 517-529 ◽  
Author(s):  
S. B. G. Eysenck
Keyword(s):  
Experimental Analysis ◽  
Physical Symptoms ◽  
The Other ◽  
Diagnostic Classification ◽  
Cognitive Deterioration ◽  
Mixed States ◽  
Autonomic Imbalance ◽  
Neurotic Disorders ◽  
Other Hand ◽  
The Relationship

The problem we are concerned with is the relationship between neurosis and psychosis. It is well known psychiatrically that many patients tend to be what are called “mixed” states, meaning that the diagnostic classification is doubtful. Patients complaining of physical symptoms, such as sleeplessness, heart palpitations, and other signs of autonomic imbalance, accompanied by anxiety or phobias, and who seem well reality-oriented, are not hallucinated or deluded and do not show any cognitive deterioration, are classed as neurotics. Psychotics, on the other hand, are generally deluded and hallucinated, are poorly reality-oriented, tend to show signs of cognitive deterioration, but have an absence of the physical symptoms so characteristic of neurotic disorders.

scholarly journals Multiworld motives by closed time-like curves

2021 ◽  
Vol 2081 (1) ◽  
pp. 012029
Author(s):  
A V Shepelin ◽  
A M Rostom ◽  
V A Tomilin ◽  
L V Il’ichov
Keyword(s):  
Quantum System ◽  
Quantum State ◽  
Quantum Systems ◽  
The Other ◽  
Preparation Procedure ◽  
Time Interval ◽  
New Model ◽  
Other Hand ◽  
The Future ◽  
Compare And Contrast

Abstract We propose a new model, entitled S-CTC, for description of quantum systems in the presence of CTC – closed time-like curves. The model is based on the viewpoint on any quantum state as an observer’s state of knowledge of the system preparation procedure. We compare and contrast our S-CTC model with D-CTC and P-CTC models and show that S-CTC shares special quantum features with both D-CTC and P-CTC. As far as the interaction of the quantum system with itself coming from the future concerns, S-CTC is formally equivalent to P-CTC. On the other hand, when calculating outcome probabilities for a measurement within the time interval between the entrance and exit of CTC, S-CTC becomes equivalent to D-CTC. Both these models require the concept of alternative realities (worlds) where different measurement outcomes are recorded and alternative connections of these realities by CTC.

scholarly journals Effects of Indistinguishability in a System of Three Identical Qubits

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alessia Castellini ◽  
Rosario Franco ◽  
Giuseppe Compagno
Keyword(s):  
Quantum State ◽  
Identical Particle ◽  
Quantum Correlations ◽  
The Other ◽  
Standard Approach ◽  
Identical Particles ◽  
Spatial Overlap ◽  
Other Hand ◽  
Elementary State

Quantum correlations of identical particles are important for quantum-enhanced technologies. The recently introduced non-standard approach to treat identical particles is here exploited to show the effect of particle indistinguishability on the characterization of entanglement of three identical qubits. We show that, by spatially localized measurements in separated regions, three independently-prepared separated qubits in a pure elementary state behave as distinguishable ones, as expected. On the other hand, delocalized measurements make it emerge a measurement-induced entanglement. We then find that three independently-prepared boson qubits under complete spatial overlap exhibit genuine three-partite entanglement. These results evidence the effect of spatial overlap on identical particle entanglement and show that the latter depends on both the quantum state and the type of measurement.

scholarly journals A system of axiomatic set theory. Part IV. General set theory

1942 ◽  
Vol 7 (4) ◽  
pp. 133-145 ◽  
Author(s):  
Paul Bernays
Keyword(s):  
Set Theory ◽  
Axiom Of Choice ◽  
Point Of View ◽  
The Other ◽  
Von Neumann ◽  
Neumann System ◽  
Other Hand ◽  
The Axiom Of Choice ◽  
Axiomatic Set Theory

Our task in the treatment of general set theory will be to give a survey for the purpose of characterizing the different stages and the principal theorems with respect to their axiomatic requirements from the point of view of our system of axioms. The delimitation of “general set theory” which we have in view differs from that of Fraenkel's general set theory, and also from that of “standard logic” as understood by most logicians. It is adapted rather to the tendency of von Neumann's system of set theory—the von Neumann system having been the first in which the possibility appeared of separating the assumptions which are required for the conceptual formations from those which lead to the Cantor hierarchy of powers. Thus our intention is to obtain general set theory without use of the axioms V d, V c, VI.It will also be desirable to separate those proofs which can be made without the axiom of choice, and in doing this we shall have to use the axiom V*—i.e., the theorem of replacement taken as an axiom. From V*, as we saw in §4, we can immediately derive V a and V b as theorems, and also the theorem that a function whose domain is represented by a set is itself represented by a functional set; and on the other hand V* was found to be derivable from V a and V b in combination with the axiom of choice. (These statements on deducibility are of course all on the basis of the axioms I–III.)

scholarly journals NLO QCD and EW corrections to vector-boson scattering into ZZ at the LHC

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Ansgar Denner ◽  
Robert Franken ◽  
Mathieu Pellen ◽  
Timo Schmidt
Keyword(s):  
Phase Space ◽  
Cross Section ◽  
Vector Boson ◽  
Z Bosons ◽  
The Other ◽  
Leading Order ◽  
Order Analysis ◽  
Other Hand ◽  
Vector Boson Scattering ◽  
Take All

Abstract We present the first calculation of the full next-to-leading-order electroweak and QCD corrections for vector-boson scattering (VBS) into a pair of Z bosons at the LHC. We consider specifically the process pp → e+e−μ+μ−jj + X at orders $$ \mathcal{O} $$ O (α7) and $$ \mathcal{O} $$ O (αsα6) and take all off-shell and interference contributions into account. Owing to the presence of enhanced Sudakov logarithms, the electroweak corrections amount to −16% of the leading-order electroweak fiducial cross section and induce significant shape distortions of differential distributions. The QCD corrections on the other hand are larger (+24%) than typical QCD corrections in VBS. This originates from considering the full computation including tri-boson contributions in a rather inclusive phase space. We also provide a leading-order analysis of all contributions to the cross section for pp → e+e−μ+μ−jj + X in a realistic setup.

Optimal class-specific witnesses for three-qubit entanglement from Greenberger-Horne-Zeilinger symmetry

2013 ◽  
Vol 13 (3&4) ◽  
pp. 210-220
Author(s):  
Christopher Eltschka ◽  
Jens Siewert
Keyword(s):  
Ghz State ◽  
Quantum States ◽  
Point Of View ◽  
The Other ◽  
Mixed States ◽  
Other Hand ◽  
New Type ◽  
The One ◽  
Qubit States ◽  
Symmetric States

Recently, a new type of symmetry for three-qubit quantum states was introduced, the so-called Greenberger-Horne-Zeilinger (GHZ) symmetry. It includes the operations which leave the three-qubit standard GHZ state unchanged. This symmetry is powerful as it yields families of mixed states that are, on the one hand, complex enough from the physics point of view and, on the other hand, simple enough mathematically so that their properties can be characterized analytically. We show that by using the properties of GHZ-symmetric states it is straightforward to derive optimal witnesses for detecting class-specific entanglement in arbitrary three-qubit states.

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