New correlation relations in classical and quantum systems with different numbers of subsystems1

Doskoch, Igor Ya.; Man’ko, Margarita A.

doi:10.1088/1742-6596/1612/1/012011

Cited by 6 publications

(4 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this formalism, it is possible to use the probability representation of quantum states [16,20,[36][37][38][39] and expressions of quantum states in terms of the Jordan-Schwinger map [40,41], where the spin states are given in the form of two-mode oscillator wave functions. This so-called Hermite polynomial representation of spin states [42][43][44] is formulated as the probability distribution of oscillator quantum states.…”

Section: Discussionmentioning

confidence: 99%

Pseudo-Qutrit Formed by Two Interacting Identical Spins (s = 1/2) in a Variable External Magnetic Field

Belousov

Igor

Vladimir

2023

Entropy

View full text Add to dashboard Cite

An analytical solution is obtained for the problem of two interacting, identical but separated spin 1/2 particles in a time-dependent external magnetic field, in a general case. The solution involves isolating the pseudo-qutrit subsystem from a two-qubit system. It is shown that the quantum dynamics of a pseudo-qutrit system with a magnetic dipole–dipole interaction can be described clearly and accurately in an adiabatic representation, using a time-dependent basis set. The transition probabilities between the energy levels for an adiabatically varying magnetic field, which follows the Landau–Majorana–Stuckelberg–Zener (LMSZ) model within a short time interval, are illustrated in the appropriate graphs. It is shown that for close energy levels and entangled states, the transition probabilities are not small and strongly depend on the time. These results provide insight into the degree of entanglement of two spins (qubits) over time. Furthermore, the results are applicable to more complex systems with a time-dependent Hamiltonian.

show abstract

Section: Discussionmentioning

confidence: 99%

Pseudo-Qutrit Formed by Two Interacting Identical Spins (s = 1/2) in a Variable External Magnetic Field

Belousov

Igor

Vladimir

2023

Entropy

View full text Add to dashboard Cite

show abstract

“…We can therefore consider the equality ( 53 ) as a realization of the inequality ( 54 ) for two identical qubits in state ( 46 ) at

. Furthermore, the relation ( 53 ) can be treated as the Born rule for two qubits [ 66 , 67 , 68 ].…”

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Belousov

Man’ko

Migliore

et al. 2022

Entropy

View full text Add to dashboard Cite

We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole–dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.

show abstract

“…The coherent state tomogram at t = 0 is given by Eqs. ( 25)- (27). Employing the replacement μ → μ and ν → ν + μt in all formulas for the ground and coherent states of the oscillator and the Schrödinger cat state, we arrive at the results for tomograms of the corresponding free-particle states.…”

Section: The Evolution Of Free-particle Cat Statesmentioning

confidence: 99%

“…where tomograms w ±α 1 and w ±α 2 are probability distributions of two oscillators given by Eqs. ( 25)- (27). We can also consider the wave function of the form…”

Section: Cat States Of Two Oscillatorsmentioning

confidence: 99%

Even and Odd Schrödinger Cat States in the Probability Representation of Quantum Mechanics

Ádám

Man’ko

2022

J Russ Laser Res

Self Cite

View full text Add to dashboard Cite

We consider even and odd coherent states (Schrödinger cat states) in the probability representation of quantum mechanics. The probability representation of the cat states is explicitly given using the formalism of quantizer and dequantizer operators, that provides the existence of an invertible map of operators acting in a Hilbert space onto functions called symbols of the operators. We employ a special set of quantizers and dequantizers to construct Wigner functions of the Schrödinger cat states and obtain the relation of the Wigner functions and the probability distributions by means of the Radon integral transform. The notion of entangled classical probability distributions is introduced in probability theory.

show abstract

New correlation relations in classical and quantum systems with different numbers of subsystems1

Cited by 6 publications

References 60 publications

Pseudo-Qutrit Formed by Two Interacting Identical Spins (s = 1/2) in a Variable External Magnetic Field

Pseudo-Qutrit Formed by Two Interacting Identical Spins (s = 1/2) in a Variable External Magnetic Field

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Even and Odd Schrödinger Cat States in the Probability Representation of Quantum Mechanics

Contact Info

Product

Resources

About