arXiv subjects
Publications and source records attributed to Eylee Jung.
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.
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.
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 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 $\rho$ (state for target absence) and $\sigma$ (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 $N_S < 0.295$.
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 R\'{e}nyi 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 $\alpha$. While the von Neumann entropy with $\alpha = 0$ 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 $\alpha \neq 0$. The R\'{e}nyi entropy $S_{\gamma}$ with nonzero $\alpha$ also exhibits similar behavior at the large temperature region. In this region the R\'{e}nyi entropy exhibit decreasing behavior with increasing the temperature. The decreasing rate becomes larger when the order of the R\'{e}nyi entropy $\gamma$ is smaller.
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.
We introduce two tangle-based four-party entanglement measures $t_1$ and $t_2$, and two negativity-based measures $n_1$ and $n_2$, which are derived from the monogamy relations. These measures are computed for three four-qubit maximally entangled and W states explicitly. We also compute these measures for the rank-$2$ mixture $ρ_4 = p \ket{\mbox{GHZ}_4} \bra{\mbox{GHZ}_4} + (1 - p) \ket{\mbox{W}_4} \bra{\mbox{W}_4}$ by finding the corresponding optimal decompositions. It turns out that $t_1 (ρ_4)$ is trivial and the corresponding optimal decomposition is equal to the spectral decomposition. Probably, this triviality is a sign of the fact that the corresponding monogamy inequality is not sufficiently tight. We fail to compute $t_2 (ρ_4)$ due to the difficulty for the calculation of the residual entanglement. The negativity-based measures $n_1 (ρ_4)$ and $n_2 (ρ_4)$ are explicitly computed and the corresponding optimal decompositions are also derived explicitly.
We examine mixedness and entanglement of the chronology-respecting (CR) system with assuming that quantum mechanical closed timelike curves (CTCs) exist in nature and by introducing the qubit system and applying the general controlled operations between CR and CTC systems. We use the magnitude of Bloch vector as a measure of mixedness. While Deutschian-CTC (D-CTC) either preserves or decreases the magnitude, postselected-CTC (P-CTC) can increases it. Nonintuitively, even the completely mixed CR-qubit can be converted into a pure state after CTC-qubit travels around the P-CTC. It is also shown that while D-CTC cannot increase the entanglement of CR system, P-CTC can increase it. Surprisingly, any partially entangled state can be maximally entangled pure state if P-CTC exists. Thus, distillation of P-CTC-assisted entanglement can be easily achieved without preparing the multiple copies of the partially entangled state.
It is known that there are three maximally entangled states $\ket{Φ_1} = (\ket{0000} + \ket{1111}) / \sqrt{2}$, $\ket{Φ_2} = (\sqrt{2} \ket{1111} + \ket{1000} + \ket{0100} + \ket{0010} + \ket{0001}) / \sqrt{6}$, and $\ket{Φ_3} = (\ket{1111} + \ket{1100} + \ket{0010} + \ket{0001}) / 2$ in four-qubit system. It is also known that there are three independent measures ${\cal F}^{(4)}_j \hspace{.2cm} (j=1,2,3)$ for true four-way quantum entanglement in the same system. In this paper we compute ${\cal F}^{(4)}_j$ and their corresponding linear monotones ${\cal G}^{(4)}_j$ for three rank-two mixed states $ρ_j = p \ket{Φ_j}\bra{Φ_j} + (1 - p) \ket{\mbox{W}_4} \bra{\mbox{W}_4}$, where $\ket{\mbox{W}_4} = (\ket{0111} + \ket{1011} + \ket{1101} + \ket{1110}) / 2$. We discuss the possible applications of our results briefly.
It is well-known that entanglement of formation (EOF) and relative entropy of entanglement (REE) are exactly identical for all two-qubit pure states even though their definitions are completely different. We think this fact implies that there is a veiled connection between EOF and REE. In this context, we suggest a procedure, which enables us to compute REE from EOF without relying on the converse procedure. It is shown that the procedure yields correct REE for many symmetric mixed states such as Bell-diagonal, generalized Vedral-Plenino, and generalized Horodecki states. It also gives a correct REE for less symmetric Vedral-Plenio-type state. However, it is shown that the procedure does not provide correct REE for arbitrary mixed states.
An entanglement monotone, which is invariant under the determinant 1 SLOCC operations and measures the true quadripartite entanglement, is explicitly constructed.