Concentration of Measure for Quantum States with a Fixed Expectation Value

For bipartite quantum states we obtain lower bounds on two important entanglement measures, concurrence and negativity, studying the inequalities for the expectation value of a projector on some subspace of the Hilbert space. Several applications, including analysis of stability of entanglement under various perturbations of a state, are discussed.

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Entropic Characterization of Quantum States with Maximal Evolution under Given Energy Constraints

Entropy ◽

10.3390/e21080770 ◽

2019 ◽

Vol 21 (8) ◽

pp. 770 ◽

Cited By ~ 2

Author(s):

Ana P. Majtey ◽

Andrea Valdés-Hernández ◽

César G. Maglione ◽

Angel R. Plastino

Keyword(s):

Energy Distribution ◽

Variational Problem ◽

Quantum System ◽

Dynamical Evolution ◽

Quantum States ◽

Time Interval ◽

Expectation Value ◽

Energy Constraints ◽

Pure Quantum State

A measure D [ t 1 , t 2 ] for the amount of dynamical evolution exhibited by a quantum system during a time interval [ t 1 , t 2 ] is defined in terms of how distinguishable from each other are, on average, the states of the system at different times. We investigate some properties of the measure D showing that, for increasing values of the interval’s duration, the measure quickly reaches an asymptotic value given by the linear entropy of the energy distribution associated with the system’s (pure) quantum state. This leads to the formulation of an entropic variational problem characterizing the quantum states that exhibit the largest amount of dynamical evolution under energy constraints given by the expectation value of the energy.

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Breakdown of the equivalence between gravitational mass and energy due to quantum effects

International Journal of Modern Physics D ◽

10.1142/s0218271819300209 ◽

2019 ◽

Vol 28 (12) ◽

pp. 1930020 ◽

Cited By ~ 2

Author(s):

Andrei G. Lebed

Keyword(s):

Degrees Of Freedom ◽

Quantum States ◽

Gravitational Mass ◽

Electron Mass ◽

Expectation Values ◽

Expectation Value ◽

State Formula ◽

Stationary Quantum ◽

Passive Gravitational Mass ◽

Internal Degrees Of Freedom

We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in the semiclassical variant of general relativity, where the gravitational field is not quantized but matter is quantized. To this end, we consider the simplest quantum body with internal degrees of freedom — a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is the inequivalence between passive gravitational mass and energy at the microscopic level. Indeed, the quantum measurement of gravitational mass can give a result which is different from the expected one, [Formula: see text], where the electron is initially in its ground state; [Formula: see text] is the bare electron mass. The second effect is that the expectation values of both the passive and active gravitational masses of stationary quantum states are equivalent to the expectation value of the energy. The most spectacular effects are the inequivalence of the passive and active gravitational masses and the energy at the macroscopic level for an ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by Einstein’s famous equation, [Formula: see text]. In this paper, we also improve several drawbacks of the original pioneering works.

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Instantaneous Quantum Description of Photonic Wavefronts and Applications

10.20944/preprints201811.0196.v1 ◽

2018 ◽

Author(s):

Andre Vatarescu

Keyword(s):

Quantum States ◽

Expectation Values ◽

Direct Evaluation ◽

Expectation Value ◽

Quantum Description ◽

Instantaneous Phase ◽

Consecutive Number ◽

Phase Sensitive ◽

Pure States ◽

Phase Sensitive Amplification

By imposing the condition of non-vanishing expectation values for the amplitude and phase of field operators, pure quantum states are identified composed of two consecutive number states.  These pure states also deliver noise-free radiation modes restricting the “half-photon noise” to the expectation value of the lowest level of dynamic and coherent number states. As a result, instantaneous phase-sensitive amplification of photons is easily controlled   and   direct evaluation of time or distance - varying wavefront distributions of photons and phases can be carried out for sub-Poissonian distributions of photons without the need for quasi-probabilities.

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Breakdown of the equivalence between gravitational mass and energy for a quantum body: Theory and suggested experiments

International Journal of Modern Physics D ◽

10.1142/s021827181530027x ◽

2015 ◽

Vol 24 (11) ◽

pp. 1530027 ◽

Cited By ~ 4

Author(s):

Andrei G. Lebed

Keyword(s):

Microscopic Level ◽

Quantum States ◽

Gravitational Mass ◽

Expectation Values ◽

Expectation Value ◽

Stationary Quantum ◽

Body Theory ◽

Passive Gravitational Mass ◽

Theoretical Results ◽

Active Gravitational Mass

In this paper, we review recent theoretical results, obtained for the equivalence between gravitational mass and energy of a composite quantum body as well as for its breakdown at macroscopic and microscopic levels. In particular, we discuss that the expectation values of passive and active gravitational mass operators are equivalent to the expectation value of energy for electron stationary quantum states in hydrogen atom. On the other hand, for superpositions of the stationary quantum states, inequivalence between the gravitational masses and energy appears at a macroscopic level. It reveals itself as time-dependent oscillations of the expectation values of passive and active gravitational masses, which can be, in principle, experimentally measured. Inequivalence between passive gravitational mass and energy at a microscopic level can be experimentally observed as unusual electromagnetic radiation, emitted by a macroscopic ensemble of the atoms. We propose the corresponding experiment, which can be done on the Earth's orbit, using small spacecraft. If such experiment is done it would be the first direct observation of quantum effects in general relativity.

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Correlation analysis of radiation damage

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108210 ◽

1978 ◽

Vol 36 (1) ◽

pp. 214-215

Author(s):

R. Hegerl ◽

A. Feltynowski ◽

B. Grill

Keyword(s):

Electron Microscopy ◽

Independent Random Variables ◽

Optical Parameters ◽

Bright Field Image ◽

Bright Field ◽

Expectation Value ◽

All Optical ◽

Image Element ◽

Stochastic Series ◽

The Common

Till now correlation functions have been used in electron microscopy for two purposes: a) to find the common origin of two micrographs representing the same object, b) to check the optical parameters e. g. the focus. There is a third possibility of application, if all optical parameters are constant during a series of exposures. In this case all differences between the micrographs can only be caused by different noise distributions and by modifications of the object induced by radiation.Because of the electron noise, a discrete bright field image can be considered as a stochastic series Pm,where i denotes the number of the image and m (m = 1,.., M) the image element. Assuming a stable object, the expectation value of Pm would be Ηm for all images. The electron noise can be introduced by addition of stationary, mutual independent random variables nm with zero expectation and the variance. It is possible to treat the modifications of the object as a noise, too.

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