arXiv subjects
Publications and source records attributed to DaeKil Park.
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in the Arthurs-Kelly system. The Feynman propagator for this system is exactly derived within the first order of the GUP parameter $\beta$. The application of it in the early universe stage is briefly discussed.
Superconductors at temperatures below the critical temperature $T_c$ can be modeled as a mixture of Fermi and Bose gases, where the Fermi gas consists of conduction electrons and the Bose gas comprises Cooper pairs. This simple model enables the computation of the temperature dependence of $2 r(T) / N$, where $N$ is the total number of conduction electrons and $r(T)$ is the number of Cooper pairs at temperature $T$. Analyzing $2 r(T) / N$ across various superconductors may provide significant insights into the mechanisms behind high-temperature superconductivity, especially regarding coherence in Cooper pairs.
The generalized version of the Arthurs-Kelly inequality is derived when the initial state is a tripartite separable state. When each initial substate obeys the minimal uncertainty, the generalized version reduces to the well-known inequality, i.e. twice of the Heisenberg uncertainty. If the initial probe state is entangled, it is shown that the generalized version of the Arthurs-Kelly inequality can be violated. We show the violation explicitly by introducing a special example.
Quantum illumination with asymmetric strategy is examined by making use of the three-mode maximally entangled Gaussian state, which involves one signal and two idler beams. It is shown that this scenario gives less-error probability compared to that with the two-mode squeezed vacuum state when $N_S$, average photon number per signal, is less than $0.46$.
We develop the Euclidean time method of the variational quantum eigensolver for solving the generalized eigenvalue equation $A \ket{\phi_n} = \lambda_n B \ket{\phi_n}$, where $A$ and $B$ are hermitian operators, and $\ket{\phi_n}$ and $\lambda_n$ are called the eigenvector and the corresponding eigenvalue of this equation respectively. For the purpose we modify the usual Euclidean time formalism, which was developed for solving the time-independent Schr\"{o}dinger equation. We apply our formalism to three numerical examples for test. It is shown that our formalism works very well in all numerical examples. We also apply our formalism to the hydrogen atom and compute the electric polarizability. It turns out that our result is slightly less than that of the perturbation method.
In this paper we examine the average R\'{e}nyi entropy $S_{\alpha}$ of a subsystem $A$ when the whole composite system $AB$ is a random pure state. We assume that the Hilbert space dimensions of $A$ and $AB$ are $m$ and $m n$ respectively. First, we compute the average R\'{e}nyi entropy analytically for $m = \alpha = 2$. We compare this analytical result with the approximate average R\'{e}nyi entropy, which is shown to be very close. For general case we compute the average of the approximate R\'{e}nyi entropy $\widetilde{S}_{\alpha} (m,n)$ analytically. When $1 \ll n$, $\widetilde{S}_{\alpha} (m,n)$ reduces to $\ln m - \frac{\alpha}{2 n} (m - m^{-1})$, which is in agreement with the asymptotic expression of the average von Neumann entropy. Based on the analytic result of $\widetilde{S}_{\alpha} (m,n)$ we plot the $\ln m$-dependence of the quantum information derived from $\widetilde{S}_{\alpha} (m,n)$. It is remarkable to note that the nearly vanishing region of the information becomes shorten with increasing $\alpha$, and eventually disappears in the limit of $\alpha \rightarrow \infty$. The physical implication of the result is briefly discussed.
Scrambling is a concept introduced from information loss problem arising in black hole. In this paper we discuss the effect of scrambling from a perspective of pure quantum information theory. We introduce $7$-qubit quantum circuit for a quantum teleportation. It is shown that the teleportation can be perfect if a maximal scrambling unitary is used. From this fact we conjecture that ``the quantity of scrambling is proportional to the fidelity of teleportation''. In order to confirm the conjecture we introduce $\theta$-dependent partially scrambling unitary, which reduces to no scrambling and maximal scrambling at $\theta = 0$ and $\theta = \pi / 2$, respectively. Then, we compute the average fidelity analytically, and numerically by making use of qiskit (version $0.36.2$) and $7$-qibit real quantum computer ibm$\_$oslo. Finally, we conclude that our conjecture can be true or false depending on the choice of qubits for Bell measurement.
The role of entanglement is discussed in the Harrow-Hassidim-Lloyd (HHL) algorithm. We compute all tripartite entanglement at every steps of the HHL algorithm. The tripartite entanglement is generated in the first quantum phase estimation (QPE) step. However, it turns out that amount of the generated entanglement is not maximal except very rare cases. In the second rotation step some tripartite entanglement is annihilated. Thus, the net tripartite entanglement is diminished. At the final inverse-QPE step the matrix inversion task is completed at the price of complete annihilation of the entanglement. An implication of this result is discussed.
The quantum illumination is examined by making use of the three-mode maximally entangled Gaussian state, which involves one signal and two idler beams. It is shown that the quantum Bhattacharyya bound between $ρ$ (state for target absence) and $σ$ (state for target presence) is less than the previous result derived by two-mode Gaussian state when $N_S$, average photon number per signal, is less than $0.295$. This indicates that the quantum illumination with three-mode Gaussian state gives less error probability compared to that with two-mode Gaussian state when $N_S < 0.295$.
We explore how the quantum entanglement is modified in the generalized uncertainty principle (GUP)-corrected quantum mechanics by introducing the coupled harmonic oscillator system. Constructing the ground state $ρ_0$ and its reduced substate $ρ_A = \mbox{Tr}_B ρ_0$, we compute two entanglement measures of $ρ_0$, i.e. ${\cal E}_{EoF} (ρ_0) = S_{von} (ρ_A)$ and ${\cal E}_γ (ρ_0) = S_γ (ρ_A)$, where $S_{von}$ and $S_γ$ are the von Neumann and Rényi entropies, up to the first order of the GUP parameter $α$. It is shown that ${\cal E}_γ (ρ_0)$ increases with increasing $α$ when $γ= 2, 3, \cdots$. The remarkable fact is that ${\cal E}_{EoF} (ρ_0)$ does not have first-order of $α$. Based on there results we conjecture that ${\cal E}_γ (ρ_0)$ increases or decreases with increasing $α$ when $γ> 1$ or $γ< 1$ respectively for nonnegative real $γ$.
It is well-known that quantum illumination with a two-mode squeezed vacuum state as an initial entangled bipartite state achieves $6$ dB quantum advantage in the error probability compared to classical coherent-state illumination. Is entanglement the only resource responsible for the quantum advantage? We explore this question by making use of squeezing operations. Finally, we conclude that the answer to the question is negative.
The Rényi and von Neumann entropies of the thermal state in the generalized uncertainty principle (GUP)-corrected single harmonic oscillator system are explicitly computed within the first order of the GUP parameter $α$. While the von Neumann entropy with $α= 0$ exhibits a monotonically increasing behavior in external temperature, the nonzero GUP parameter makes the decreasing behavior of the von Neumann entropy at the large temperature region. As a result, the von Neumann entropy is maximized at the finite temperature if $α\neq 0$. The Rényi entropy $S_γ$ with nonzero $α$ also exhibits similar behavior at the large temperature region. In this region the Rényi entropy exhibit decreasing behavior with increasing the temperature. The decreasing rate becomes larger when the order of the Rényi entropy $γ$ is smaller.
We discuss classical electrodynamics and the Aharonov-Bohm effect in the presence of the minimal length. In the former we derive the classical equation of motion and the corresponding Lagrangian. In the latter we adopt the generalized uncertainty principle (GUP) and compute the scattering cross section up to the first-order of the GUP parameter $β$. Even though the minimal length exists, the cross section is invariant under the simultaneous change $ϕ\rightarrow -ϕ$, $α' \rightarrow -α'$, where $ϕ$ and $α'$ are azimuthal angle and magnetic flux parameter. However, unlike the usual Aharonv-Bohm scattering the cross section exhibits discontinuous behavior at every integer $α'$. The symmetries, which the cross section has in the absence of GUP, are shown to be explicitly broken at the level of ${\cal O} (β)$.
Uncertainties $(Δx)^2$ and $(Δp)^2$ are analytically derived in an $N$-coupled harmonic oscillator system when spring and coupling constants are arbitrarily time-dependent and each oscillator is in an arbitrary excited state. When $N = 2$, those uncertainties are shown as just arithmetic average of uncertainties of two single harmonic oscillators. We call this property as "sum rule of quantum uncertainty". However, this arithmetic average property is not generally maintained when $N \geq 3$, but it is recovered in $N$-coupled oscillator systems if and only if $(N-1)$ quantum numbers are equal. The generalization of our results to a more general quantum system is briefly discussed.
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the first order of the GUP parameter.
We derive explicitly the thermal state of the two coupled harmonic oscillator system when the spring and coupling constants are arbitrarily time-dependent. In particular, we focus on the case of sudden change of frequencies. In this case we compute purity function, Rényi and von Neumann entropies, and mutual information analytically and examine their temperature-dependence. We also discuss on the thermal entanglement phase transition by making use of the negativity-like quantity. Our calculation shows that the critical temperature $T_c$ increases with increasing the difference between the initial and final frequencies. In this way we can protect the entanglement against the external temperature by introducing large difference of initial and final frequencies.
The non-relativistic quantum mechanics with the generalized uncertainty principle (GUP) is examined when the potential is one-dimensional $δ-$function. It is shown that unlike usual quantum mechanics, the Schrödinger and Feynman's path-integral approaches are inequivalent at the first order of GUP parameter.
Recently in [Phys. Rev. D $99$ $(2019)$ 104010] the non-relativistic Feynman propagator for harmonic oscillator system is presented when the generalized uncertainty principle is employed. In this short comment it is shown that the expression is incorrect. We also derive the correct expression of it.