arXiv subjects

Hong-Bin Chen

Publications and source records attributed to Hong-Bin Chen.

65 records · Page 4Linked to original sources

arXiv2018

From a Consequence of Bertrand's Postulate to Hamilton Cycles

A consequence of Bertrand's postulate, proved by L. Greenfield and S. Greenfield in 1998, assures that the set of integers $\{1,2,\cdots, 2n\}$ can be partitioned into pairs so that the sum of each pair is a prime number for any positive integer $n$. Cutting through it from the angle of Graph Theory, this paper provides new insights into the problem. We conjecture a stronger statement that the set of integers $\{1,2,\cdots, 2n\}$ can be rearranged into a cycle so that the sum of any two adjacent integers is a prime number. Our main result is that this conjecture is true for infinitely many cases.

math.CO↗

arXiv2018

Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems

One of the fundamental issues in the field of open quantum systems is the classification and quantification of non-Markovianity. In the contest of quantity-based measures of non-Markovianity, the intuition of non-Markovianity in terms of information backflow is widely discussed. However, it is not easy to characterize the information flux for a given system state and show its connection to non-Markovianity. Here, by using the concepts from thermodynamics and information theory, we discuss a potential definition of information flux of an open quantum system, valid for static environments. We present a simple protocol to show how a system attempts to share information with its environment and how it builds up system-environment correlations. We also show that the information returned from the correlations characterizes the non-Markovianity and a hierarchy of indivisibility of the system dynamics.

quant-ph↗

arXiv2018

Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics

The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment correlations by examining the system dynamics alone. Our approach is based on the possibility or impossibility to simulate open-system dynamics with Hamiltonian ensembles. As we show, such (im)possibility to simulate is closely linked to the system-environment correlations. We thus define the nonclassicality of open-system dynamics in terms of the nonexistence of a Hamiltonian-ensemble simulation. This classifies any nonunital open-system dynamics as nonclassical. We give examples for open-system dynamics that are unital and classical, as well as unital and nonclassical.

quant-ph↗

arXiv2017

Hierarchy of Non-Markovianity and $k$-divisibility phase diagram of Quantum Processes in Open Systems

In recent years, much effort has been devoted to the construction of a proper measure of quantum non-Markovianity. However, those proposed measures are shown to be at variance with different situations. In this work, we utilize the theory of $k$-positive maps to generalize a hierarchy of $k$-divisibility and develop a powerful tool, called $k$-divisibility phase diagram, which can provide a further insight into the nature of quantum non-Markovianity. By exploring the phase diagram with several paradigms, we can explain the origin of the discrepancy between two frequently used measures and find the condition under which the two measures coincide with each other.

quant-ph↗

arXiv2017

Temporal Steering in Four Dimensions with applications to coupled qubits and magnetoreception

Einstein-Podolsky-Rosen (EPR) steering allows Alice to remotely prepare a state in some specific bases for Bob through her choice of measurements. The temporal analogue of EPR steering, temporal steering, also reveals the steerability of a single system between different times. Focusing on a four-dimensional system, here we investigate the dynamics of the temporal steering measures, the temporal steering robustness, using 5 mutually unbiased bases. As an example of an application, we use these measures to examine the temporal correlations in a radical pair model of magnetoreception. We find that, due to interactions with a static nuclear spin, the radical pair model exhibits strong non-Markovianity.

quant-ph↗

arXiv2016

Vibration-induced coherence enhancement of the performance of a biological quantum heat engine

Photosynthesis has been a long-standing research interest due to its fundamental importance. Recently, studies on photosynthesis processes also have inspired attention from a thermodynamical aspect when considering photosynthetic apparatuses as biological quantum heat engines. Quantum coherence is shown to play a crucial role in enhancing the performance of these quantum heat engines. Based on the experimentally reported structure, we propose a quantum heat engine model with a non-Markovian vibrational mode. We show that one can obtain a performance enhancement easily for a wide range of parameters in the presence of the vibrational mode. Our results provide insights into the photosynthetic processes and a design principle mimicking natural organisms.

physics.chem-ph↗

arXiv2016

Families of Subsets Without a Given Poset in the Interval Chains

For two posets $P$ and $Q$, we say $Q$ is $P$-free if there does not exist any order-preserving injection from $P$ to $Q$. The speical case for $Q$ being the Boolean lattice $B_n$ is well-studied, and the optiamal value is denoted as $\lanp$. Let us define $\La(Q,P)$ to be the largest size of any $P$-free subposet of $Q$. In this paper, we give an upper bound for $\La(Q,P)$ when $Q$ is a double chain and $P$ is any graded poset, which is better than the previous known upper bound, by means of finding the indpendence number of an auxiliary graph related to $P$. For the auxiliary graph, we can find its independence number in polynomial time. In addition, we give methods to construct the posets satisfying the Griggs-Lu conjecture.

math.CO↗

arXiv2015

Using non-Markovian measures to evaluate quantum master equations for photosynthesis

When dealing with system-reservoir interactions in an open quantum system, such as a photosynthetic light-harvesting complex, approximations are usually made to obtain the dynamics of the system. One question immediately arises: how good are these approximations, and in what ways can we evaluate them? Here, we propose to use entanglement and a measure of non-Markovianity as benchmarks for the deviation of approximate methods from exact results. We apply two frequently-used perturbative but non-Markovian approximations to a photosynthetic dimer model and compare their results with that of the numerically-exact hierarchy equation of motion (HEOM). This enables us to explore both entanglement and non-Markovianity measures as means to reveal how the approximations either overestimate or underestimate memory effects and quantum coherence. In addition, we show that both the approximate and exact results suggest that non-Markonivity can, counter-intuitively, increase with temperature, and with the coupling to the environment.

quant-ph↗

arXiv2015

Multi-stability and condensation of exciton-polaritons below threshold

Exciton-polaritons can condense to a macroscopic quantum state through a non-equilibrium process of pumping and decay. In recent experiments, polariton condensates are used to observe, for a short time, nonlinear Josephson phenomena by coupling two condensates. However, it is still not clear how these phenomena are affected by the pumping and decay at long times and how the coupling alters the polariton condensation. Here, we consider a polariton Josephson junction pumped on one side and study its dynamics within a mean-field theory. The Josephson current is found to give rise to multi-stability of the stationary states, which are sensitive to the initial conditions and incoherent noises. These states can be attributed to either the self-trapping effect or the parity-time (PT) symmetry of the system. These results can be used to explain the emission spectra and the $π$-phase locking observed in recent experiments. We further predict that the multi-stability can reduce to the self-trapped state if the PT symmetry is broken. Moreover, the polaritons can condense even below the threshold, exhibiting hysteresis.

quant-ph↗

arXiv2014

Multi-Group Testing for Items with Real-Valued Status under Standard Arithmetic

This paper proposes a novel generalization of group testing, called multi-group testing, which relaxes the notion of "testing subset" in group testing to "testing multi-set". The generalization aims to learn more information of each item to be tested rather than identify only defectives as was done in conventional group testing. This paper provides efficient nonadaptive strategies for the multi-group testing problem. The major tool is a new structure, $q$-ary additive $(w,d)$-disjunct matrix, which is a generalization of the well-known binary disjunct matrix introduced by Kautz and Singleton in 1964.

cs.IT↗

arXiv2014

On-Line Choice Number of Complete Multipartite Graphs: an Algorithmic Approach

This paper studies the on-line choice number on complete multipartite graphs with independence number $m$. We give a unified strategy for every prescribed $m$. Our main result leads to several interesting consequences comparable to known results. (1) If $ k_1-\sum_{p=2}^m(\frac{p^2}{2}-\frac{3p}{2}+1)k_p\geq 0$, where $k_p$ denotes the number of parts of cardinality $p$, then $G$ is on-line chromatic-choosable. (2) If $ |V(G)|\leq\frac{m^2-m+2}{m^2-3m+4}χ(G)$, then $G$ is on-line chromatic-choosable. (3) The on-line choice number of regular complete multipartite graphs $K_{m\star k}$ is at most $(m+\frac{1}{2}-\sqrt{2m-2})k$ for $m\geq 3$.

math.CO↗