Extended space expectation values of position related operators for hydrogen-like quantum system evolutions

It is well known that entanglement under Lorentz boosts is highly dependent on the boost scenario in question. For single-particle states, a spin-momentum product state can be transformed into an entangled state. However, entanglement is just one of the aspects that completely characterizes a quantum system. The other two are known as the wave-particle duality. Although the entanglement entropy does not remain invariant under Lorentz boosts, and neither do the measures of predictability and coherence, we show here that these three measures taken together, in a complete complementarity relation (CCR), are Lorentz invariant. Peres et al. (Peres et al. 2002 Phys. Rev. Lett. 88 , 230402. ( doi:10.1103/PhysRevLett.88.230402 )) realized that even though it is possible to formally define spin in any Lorentz frame, there is no relationship between the observable expectation values in different Lorentz frames. Analogously, one can, in principle, define complementary relations in any Lorentz frame, but there is no obvious transformation law relating complementary relations in different frames. However, our result shows that the CCRs have the same value in any Lorentz frame, i.e. there is a transformation law connecting the CCRs. In addition, we explore relativistic scenarios for single and two-particle states, which helps in understanding the exchange of different aspects of a quantum system under Lorentz boosts.

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Massively Parallel Classical Logic via Coherent Dynamics of an Ensemble of Quantum Systems with Dispersion in Size

10.26434/chemrxiv.12370538 ◽

2020 ◽

Author(s):

Hugo Gattuso ◽

Raphael D. Levine ◽

Francoise Remacle

Keyword(s):

Quantum System ◽

Quantum Dynamics ◽

Algebraic Theory ◽

Laser Pulses ◽

Quantum Systems ◽

Individual Variability ◽

Expectation Values ◽

Charge Transfer Excitons ◽

Simultaneous Reading ◽

Size Dispersion

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nano systems are not quite identical and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot, QD, dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semi-conducting QDs suggests that the dimer coherences can be probed at room temperature

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Extended space expectation values in quantum dynamical system evolutions

10.1063/1.4897873 ◽

2014 ◽

Cited By ~ 2

Author(s):

Metin Demiralp

Keyword(s):

Dynamical System ◽

Expectation Values ◽

Quantum Dynamical ◽

Quantum Dynamical System ◽

Extended Space

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On a Stroboscopic Approach to Quantum Tomography of Qudits Governed by Gaussian Semigroups

Open Systems & Information Dynamics ◽

10.1023/b:opsy.0000024756.27667.fd ◽

2004 ◽

Vol 11 (01) ◽

pp. 63-70 ◽

Cited By ~ 4

Author(s):

Andrzej Jamiołkowski

Keyword(s):

Quantum System ◽

Minimal Polynomial ◽

Quantum Tomography ◽

Expectation Values ◽

Mean Values ◽

Selfadjoint Operators ◽

The Mean

In this paper, we discuss the minimal number η of observables Q1,…, Qη, where expectation values at some time instants t1,…,tr determine the trajectory of a d-level quantum system (“qudit”) governed by the Gaussian semigroup [Formula: see text] We assume that the macroscopic information about the system in question is given by the mean values [Formula: see text] of n selfadjoint operators Q1,…, Qn at some time instants t1< t2 < … <tr, where n < d2 − 1 and r ≤ deg μ(λ, 𝕃). Here μ(λ, 𝕃) stands for the minimal polynomial of the generator [Formula: see text] of the Gaussian flow Φ(t).

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Massively Parallel Classical Logic via Coherent Dynamics of an Ensemble of Quantum Systems with Dispersion in Size

10.26434/chemrxiv.12370538.v1 ◽

2020 ◽

Cited By ~ 4

Author(s):

Hugo Gattuso ◽

Raphael D. Levine ◽

Francoise Remacle

Keyword(s):

Quantum System ◽

Quantum Dynamics ◽

Algebraic Theory ◽

Laser Pulses ◽

Quantum Systems ◽

Individual Variability ◽

Expectation Values ◽

Charge Transfer Excitons ◽

Simultaneous Reading ◽

Size Dispersion

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nano systems are not quite identical and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot, QD, dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semi-conducting QDs suggests that the dimer coherences can be probed at room temperature

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Degree of Quantumness in Quantum Synchronization

Scientific Reports ◽

10.1038/s41598-019-56468-x ◽

2019 ◽

Vol 9 (1) ◽

Cited By ~ 3

Author(s):

H. Eneriz ◽

D. Z. Rossatto ◽

F. A. Cárdenas-López ◽

E. Solano ◽

M. Sanz

Keyword(s):

Quantum Information ◽

Physical Properties ◽

Quantum System ◽

Figure Of Merit ◽

Quantum Systems ◽

Expectation Values ◽

Van Der Pol ◽

Superconducting Circuit ◽

Quantum Synchronization ◽

Van Der Pol Oscillators

AbstractWe introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators.

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Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2008170117 ◽

2020 ◽

Vol 117 (35) ◽

pp. 21022-21030 ◽

Cited By ~ 2

Author(s):

Hugo Gattuso ◽

R. D. Levine ◽

F. Remacle

Keyword(s):

Quantum System ◽

Quantum Dynamics ◽

Algebraic Theory ◽

Laser Pulses ◽

Quantum Systems ◽

Individual Variability ◽

Expectation Values ◽

Charge Transfer Excitons ◽

Simultaneous Reading ◽

Size Dispersion

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nanosystems are not quite identical, and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between theNlevels of a given quantum system can be handled as an observable. Thereby there areN2logic variables perNlevel system. This is how massive parallelism is achieved in that there areN2potential outputs for a quantum system ofNlevels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average theN2expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot (QD) dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimerNlevels include local and charge transfer excitons within each dimer. The well-studied physics of semiconducting QDs suggests that the dimer coherences can be probed at room temperature.

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