arXiv subjects

C. H. Oh

Publications and source records attributed to C. H. Oh.

At least 91 records · Page 5Linked to original sources

arXiv2012

Singularity of dynamical maps

For a dynamical map $Λ(t,0)$, which sends a state $ρ(0)$ of quantum open system to a state $ρ(t)=Λ(t,0)ρ(0)$, the decomposition law $Λ(t,0)=Λ(t,t_c)Λ(t_c,0)$ may break down at a specific time $t_c$. In this paper, we present a method to find the singular points $t_c$ and propose a measure for the singularity of the dynamical map. Two examples are portrayed to illustrate the method, the measure of singularity for these singular points is calculated and discussed. An extension to high-dimensional system is presented.

quant-ph↗

arXiv2012

Dynamical fluctuations in classical adiabatic processes: General description and their implications

Dynamical fluctuations in classical adiabatic processes are not considered by the conventional classical adiabatic theorem. In this work a general result is derived to describe the intrinsic dynamical fluctuations in classical adiabatic processes. Interesting implications of our general result are discussed via two subtopics, namely, an intriguing adiabatic geometric phase in a dynamical model with an adiabatically moving fixed-point solution, and the possible "pollution" to Hannay's angle or to other adiabatic phase objects for adiabatic processes involving non-fixed-point solutions.

physics.class-ph↗

arXiv2012

Einstein-Podolsky-Rosen Steerability Criterion for Two-Qubit Density Matrices

We propose a sufficient criterion ${S}=λ_1+λ_2-(λ_1-λ_2)^2<0$ to detect Einstein-Podolsky-Rosen steering for arbitrary two-qubit density matrix $ρ_{AB}$. Here $λ_1,λ_2$ are respectively the minimal and the second minimal eigenvalues of $ρ^{T_B}_{AB}$, which is the partial transpose of $ρ_{AB}$. By investigating several typical two-qubit states such as the isotropic state, Bell-diagonal state, maximally entangled mixed state, etc., we show this criterion works efficiently and can make reasonable predictions for steerability. We also present a mixed state of which steerability always exists, and compare the result with the violation of steering inequalities.

quant-ph↗

arXiv2012

Einstein-Podolsky-Rosen Steering in Quantum Phase Transition

We investigate the Einstein-Podolsky-Rosen (EPR) steering and its criticality in quantum phase transition. It is found that the EPR steerability function of the ground state of XY spin chain exhibits nonanalytic feature in the vicinity of a quantum phase transition by showing that its derivative with respect to anisotropy parameter diverges at the critical point. We then verify the universality of the critical phenomena of the EPR steerability function in the system. We also use two-qubit EPR-steering inequality to explore the relation between EPR steering and quantum phase transition.

quant-ph↗

arXiv2012

Quantum phase transition of two-mode Bose-Einstein condensates with an entanglement order parameter

The ground state entanglement of the two-mode Bose-Einstein condensate is investigated through a quantum phase transition approach. The entanglement measure is taken as the order parameter and this is a non-local order parameter, which is different from the conventional order parameter of the Mott insulator-superfluid phase transitions. For this non-local order parameter, scaling behavior corresponding to a continuous phase transition is obtained and a power-law divergence near the critical region follows it. This scaling behavior of quantum entanglement is analyzed by the finite-size scaling and the critical exponents are obtained as $ν= 1.01$ and $γ= 0.86$. A close connection between quantum fluctuations and the phase transition of entanglement is also obtained.

quant-ph↗

arXiv2012

Simulating Z_2 topological insulators with cold atoms in a one-dimensional optical lattice

We propose an experimental scheme to simulate and detect the properties of time-reversal invariant topological insulators, using cold atoms trapped in one-dimensional bichromatic optical lattices. This system is described by a one-dimensional Aubry-Andre model with an additional SU(2) gauge structure, which captures the essential properties of a two-dimensional Z2 topological insulator. We demonstrate that topologically protected edge states, with opposite spin orientations, can be pumped across the lattice by sweeping a laser phase adiabatically. This process constitutes an elegant way to transfer topologically protected quantum states in a highly controllable environment. We discuss how density measurements could provide clear signatures of the topological phases emanating from our one-dimensional system.

cond-mat.quant-gas↗

arXiv2011

Quantum channels that preserve the commutativity

We identify and characterize all the local quantum channels that preserves the set of classical states, i.e., does not create any quantum correlations. At first we show that the quantum correlations cannot be created from without if and only if the local quantum channel preserves the commutativity, i.e., the images of any two commuting states also commute. And then we provide an operational necessary and sufficient criterion for a known quantum channel to preserve the commutativity as well as a single observable to witness an arbitrary unknown commutativity-preserving channel. All the distance-based measures for quantum correlations, e.g., the geometric measure, are non-increasing while the quantum discord defined by von Neumann measurements can be increasing or decreasing under local commutativity-preserving channels.

quant-ph↗

arXiv2011

Minimal Kochen-Specker theorem in finite dimensions

In [1] we proved a strengthened Kochen-Specker theorem in 3 dimensions: non-contextual hidden variable (NCHV) models cannot reproduce all the quantum correlations of two compatible observables, which is a minimal requirement imposed on the NCHV models. Here we shall exclude the NCHV models with this minimal requirement in $d\ge 4$ dimensions by state-independent and experimentally testable inequalities satisfied by all NCHV models that are required to reproduce only the quantum correlations of at most two compatible observables. Furthermore our proofs use the smallest number of rays known so far, e.g., 25 (instead of 31) rays in $5$ dimensions and $5d-2\lfloor d/3\rfloor$ rays in $d\ge 6$ dimensions.

quant-ph↗

arXiv2011

Geometric entangling gates for coupled cavity system in decoherence-free subspaces

We propose a scheme to implement geometric entangling gates for two logical qubits in a coupled cavity system in decoherence-free subspaces. Each logical qubit is encoded with two atoms trapped in a single cavity and the geometric entangling gates are achieved by cavity coupling and controlling the external classical laser fields. Based on the coupled cavity system, the scheme allows the scalability for quantum computing and relaxes the requirement for individually addressing atoms.

quant-ph↗

arXiv2011

Detecting Einstein-Podolsky-Rosen Steering for Continuous Variable Wavefunctions

By use of Reid's criterion and entropic criterion, we investigate the Einstein-Podolsky-Rosen (EPR) steering for some entangled continuous variable wavefunctions. We find that not all of the entangled states violate Reid's EPR inequality and the entropic inequality, this in turn suggests that both criteria are not necessary and sufficient conditions to detect the EPR steering.

quant-ph↗

arXiv2011

Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states

We present observable lower and upper bounds for the entanglement of formation (EOF) and quantum discord (QD), which facilitates estimates of EOF and QD for arbitrary experimental unknown states in finite-dimensional bipartite systems. These bounds can be easily obtained by a few experimental measurements on a twofold copy $\varrho\otimes\varrho$ of the mixed states. Based on our results, we use the experimental measurement data of the real experiment given by Schmid \textit{et al.} [Phys. Rev. Lett. \textbf{101}, 260505 (2008)] to obtain the lower and upper bounds of EOF and QD for the experimental unknown state.

quant-ph↗

arXiv2011

Quantum No-Cloning Theorem Certified by Bell's Theorem

We investigate the connection between quantum no-cloning theorem and Bell's theorem. Designing some Bell's inequalities, we show that quantum no-cloning theorem can always be certified by Bell's theorem, and this fact in turn reflects that our physical world is essentially nonlocal.

quant-ph↗

arXiv2011

Bell Function Values Approach to Topological Quantum Phase Transitions

We investigate the relation between Bell function values (BFV) of the reduced density matrix and the topological quantum phase transitions in the Kitaev-Castelnovo-Chamon model. % [Phys. Rev. B \textbf{77}, %054433 (2008)]. We find that the first order derivative of BFV exhibits singular behavior at the critical point and we propose that it can serve as a good and convenient marker for the transition point. More interestingly, the value of the critical point can be analytically obtained in this approach. Since the BFV serves as a measure of nonlocality when it is greater than the classical bound of the correlation functions, our work has established a link between quantum nonlocality and phase transitions.

quant-ph↗

arXiv2011

Multipartite Leggett-type Inequalities

We use two different approaches to derive multipartite Leggett-type inequalities, which are generalizations of the two-qubit Leggett-type inequality obtained in [Nature Phys. \textbf{4}, 681 (2008)]. The first approach is based on the assumption that the probability distributions should be non-negative. The second approach is based on a very simple algebraic equation and is, to some extent, easier than the first approach. Although these inequalities might not be the optimal ones in the sense that their quantum violations may not be the strongest, our results make the first step of generalizing Leggett-type inequality to multi-qubit systems and provide the possibility to experimentally test non-local realism in such systems. Moreover, the two approaches here may shed new light on the challenging problem of obtaining stronger multipartite Leggett-type inequalities.

quant-ph↗

arXiv2011

Quantum phase transition in the delocalized regime of the spin-boson model

The existence of the delocalized-localized quantum phase transition (QPT) in the ohmic spin-boson model has been commonly recognized. While the physics in the localized regime is relatively simple, the delocalized regime shows many interesting behaviors. Here we reveal that in this regime there exists a novel QPT: namely, from a phase without a bound state to a phase with a bound state, which leads to completely different dynamical behaviors in these two phases. If the reservoir is initially in the displaced vacuum state (i.e., the coherent state), the spin dynamics exhibits lossless oscillation when the bound state exists; otherwise, the oscillation will decay completely. This result is compatible with the coherence-incoherence transition occurring in the small-tunneling limit. Our work indicates that the QPT physics in the spin-boson model needs further exploration.

quant-ph↗

arXiv2011

Geometric Phases for Coherent States

We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled coherent states, several interesting results followed by considering different cases for the parameters. The effects of entanglement and harmonic potential on the geometric phase are discussed.

quant-ph↗

arXiv2011

Quantum discord of two-qubit X-states

Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit X-states is proposed by Ali, Rau and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of X-states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of X-states for which their algorithm fails. And then we demonstrate that this special family of X-states provides furthermore an explicit example for the inequivalence between the minimization over positive operator-valued measures and that over von Neumann measurements.

quant-ph↗

arXiv2011

Detecting the quantum discord of an unknown state by a single observable

We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for nonzero quantum discord in $2\times N$ systems and a necessary condition in higher finite-dimensional bipartite systems. Furthermore, a nontrivial lower bound of quantum discord can be obtained from this expectation value. The proposed observable can be experimentally measured in exactly the same easy manner as that of the entanglement witness, moreover a quantum circuit is designed to determine the expectation value of our observable with four simultaneous local qubit-measurements.

quant-ph↗