Optimal control theory is developed for the task of obtaining a primary objective in a subspace of the Hilbert space while avoiding other subspaces of the Hilbert space. The primary objective can be a state-to-state transition or a unitary transformation. A new optimization functional is introduced which leads to monotonic convergence of the algorithm. This approach becomes necessary for molecular systems subject to processes implying loss of coherence such as predissociation or ionization. In these subspaces controllability is hampered or even completely lost. Avoiding the lossy channels is achieved via a functional constraint which depends on the state of the system at each instant in time. We outline the resulting new algorithm, discuss its convergence properties and demonstrate its functionality for the example of a state-to-state transition and of a unitary transformation for a model of cold Rb2.
The resource theoretic measure of quantum coherence is basis dependent, and the amount of coherence contained in a state is different in different bases. We obtained analytical solutions for the maximum coherence by optimizing the reference basis and highlighted the essential role of the mutually unbiased bases (MUBs) on attaining the maximum coherence. Apart from the relative entropy of coherence, we showed that the MUBs are optimal for the robustness of coherence, the coherence weight, and the modified skew information measure of coherence for any state. Moreover, the MUBs are optimal for al…
We provide exact analytical solutions for the problem of time-optimal transfer of coherence from one spin polarization to a three-fold coherence in a trilinear Ising chain with a fixed energy available and subject to local controls with a non negligible time cost. The time of transfer is optimal and consistent with a previous numerical result obtained assuming instantaneous local controls.
We study continuous variable coherence of phase-dependent squeezed state based on an extended Hanbury Brown-Twiss scheme. High-order coherence is continuously varied by adjusting squeezing parameter $r$, displacement $α$, and squeezing phase $θ$. We also analyze effects of background noise $γ$ and detection efficiency $η$ on the measurements. As the squeezing phase shifts from 0 to $π$, the photon statistics of the squeezed state continuously change from the anti-bunching ($g^{(n)}<1$) to super-bunching ($g^{(n)}>n!$) which shows a transition from particle nature to wave nature. The experiment…
There is generally no obvious evidence in any direct relation between photon blockade and atomic coherence. Here instead of only illustrating the photon statistics, we show an interesting relation between the steady-state photon blockade and the atomic coherence by designing a weakly driven cavity QED system with a two-level atom trapped. It is shown for the first time that the maximal atomic coherence has a perfect correspondence with the optimal photon blockade. The negative effects of the strong dissipations on photon statistics, atomic coherence and their correspondence are also addressed.…
We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schrödinger equation by using time-dependent Euler rotation together with a linear quench model to obtain the state of vacuum solution. Such state can be translated to the phase space picture to determine the Wigner distribution. We show that its Gaussian matrix $\mathbb{G}(t)$ can be used to directly cast the covariance matrix $σ(t)$. To quantify the mixedness and entanglement of the state one uses respectively linear and von Neumann entropies for three c…
We theoretically and experimentally investigate conditional enhancement of overall coherence of quantum states by probabilistic quantum operations that apply to the input state a quantum filter diagonal in the basis of incoherent states. We identify the optimal filters that for a given probability of successful filtering maximize the output coherence. We verify the performance of the studied quantum filters in a proof-of-principle experiment with linear optics, where a pair of two-level quantum systems is represented by polarization states of two photons. We comprehensively characterize the im…
We consider a method for efficient parametric generation of a laser pulse. A single laser field is injected to a three-level medium which has two lower states and one excited state. The lower states are prepared initially in a position-dependent coherent superposition state. It is shown that by proper choice of the position dependence of the superposition along the direction of propagation, the incoming field can be converted completely to a new field.
We complete the task of optimal probabilistic coherence distillation protocol, whose aim is to transform a general state into a set of n-level maximally coherent states via strictly incoherent operations (SIO). Specifically, we present the necessary and sufficient condition for the transformation from a mixed state into a pure-state ensemble via SIO. With the aid of this condition and the simplex algorithm, we can accomplish the probabilistic distillation protocol by presenting an analytical expression of the maximal average distillable coherence of a general state and constructing the corresp…
Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrate…
We propose a two-dimensional spectroscopic protocol for measuring the time-dependent coherences between the stationary states of a system induced by a time-dependent system-bath interaction. We also investigate the role of temporally-correlated noise on coherence dephasing. This protocol enables dynamical information about the system and its coupling to the environment to be determined. Our results are based on the quantum-trajectory method, and are obtained from both approximate, analytical and exact, numerical solutions of the time-dependent Schroedinger equation. As an example, we show how …
The concept of entanglement fraction is generalized to define coherence fraction of a quantum state. Precisely, it quantifies the proximity of a quantum state to maximally coherent state and it can be used as a measure of coherence. Coherence fraction has a connection with $l_1$-norm coherence and provides the criteria of coherence distillability. Optimal coherence fraction corresponding to a channel, defined from this new idea of coherence fraction, obeys a complementary relation with its decohering power. The connection between coherence fraction and $l_1$-norm coherence turns to hold for bi…
We study the remote creation of the polarization and intensity of the first-order coherence (or coherence intensity) in long spin-1/2 chains with one qubit sender and receiver. Therewith we use a physically motivated initial condition with the pure state of the sender and the thermodynamical equilibrium state of the other nodes. The main part of the creatable region is a one-to-one map of the initial-state (control) parameters, except the small subregion twice covered by the control parameters, which appears owing to the chosen initial state. The polarization and coherence intensity behave dif…
We study the properties of coherence concurrence and present a physical explanation analogous to the coherence of assistance. We give an optimal pure state decomposition which attains the coherence concurrence for qubit states. We prove the additivity of coherence concurrence under direct sum operations in another way. Using these results, we calculate analytically the coherence concurrence for X states and show its optimal decompositions. Moreover, we show that the coherence concurrence is exactly twice the convex roof extended negativity of the Schmidt correlated states, thus establishing a …
We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis is mutually unbiased with respect to the reference basis, and together with the reference basis they form an informationally complete set of measurements. We show that, in general, any strategy capable of validating quantum coherence allows one to evaluate also the exact value of coherence. We then give an explicit construction of the optimal measurements f…
The coherence time constitutes one of the most critical parameters that determines whether or not interference is observed in an experiment. For photons, it is traditionally determined by the effective spectral bandwidth of the photon. Here we report on multi-photon interference experiments in which the multi-photon coherence time, defined by the width of the interference signal, depends on the number of interfering photons and on the measurement scheme chosen to detect the particles. A theoretical analysis reveals that all multi-photon interference with more than two particles features this d…
Optimal control theory implementations for an efficient population transfer and creation of a maximum coherence in three-level system are considered. We demonstrate that the half-STIRAP (stimulated Raman adiabatic passage) scheme for creation of the maximum Raman coherence is the optimal solution according to the optimal control theory. We also present a comparative study of several implementations of optimal control theory applied to the complete population transfer and creation of the maximum coherence. Performance of the conjugate gradient method, the Zhu-Rabitz method and the Krotov method…
It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical characterization of electromagnetic radiation is isomorphic to the treatment of the orientation of a spin-1/2 particle. In this paper, motivated by Grover's original intuition and starting from this mathematical equivalence, we present a quantitative link between the geometry of time-independent optimal-speed Hamiltonian evolutions on the Bloch sphere and the geometry of…
In this work, we address the problem of maximizing fidelity in a quantum state transformation process controlled in such a way as to keep decoherence within given bounds. We consider a three-level $Λ$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We introduce fidelity as the performance index for the quantum state transformation process since the goal is to maximize the similarity of the final state density operator with the one of the desired target state. We formulate the quantum optimal control problem with state constraints where the later r…
For a quantum system undergoing a unitary process work is commonly defined based on the Two Projective Measurement (TPM) protocol which measures the energies of the system before and after the process. However, it is well known that projective measurements disregard quantum coherences of the system with respect to the energy basis, thus removing potential quantum signatures in the work distribution. Here we consider weak measurements of the system's energy difference and establish corrections to work averages arising from initial system coherences. We discuss two weak measurement protocols tha…
Roa et al. showed that quantum state discrimination between two nonorthogonal quantum states does not require quantum entanglement but quantum dissonance only. We find that quantum coherence can also be utilized for unambiguous quantum state discrimination. We present a protocol and quantify the required coherence for this task. We discuss the optimal unambiguous quantum state discrimination strategy in some cases. In particular, our work illustrates an avenue to find the optimal strategy for discriminating two nonorthogonal quantum states by measuring quantum coherence.
We investigate the ultimate precision limits for quantum phase estimation in terms of the coherence, $C$, of the probe. For pure states, we give the minimum estimation variance attainable, $V(C)$, and the optimal state, in the asymptotic limit when the probe system size, $n$, is large. We prove that pure states are optimal only if $C$ scales as $n$ with a sufficiently large proportionality factor, and that the rank of the optimal state increases with decreasing $C$, eventually becoming full-rank. We show that the variance exhibits a Heisenberg-like scaling, $V(C) \sim a_n/C^2$, where $a_n$ dec…
We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times $T_{1}$ and $T_{2}$ (associated with the longitudinal and transverse relaxations, respectively). These character…
A binary mixture of interacting Bose-Einstein condensates (BEC) in the presence of fragmentation-driving external lattice potentials forms two interdependent mean-field lattices made of each component. These effective mean-field lattices, like ordinary optical lattices, can induce additional fragmentation and phase coherence loss of BECs between lattice sites. In this study, we consider the nonequilibrium dynamics of two hyperfine states of one-dimensional Bose-Einstein condensates, subjected to state-dependent optical lattices. Our numerical calculations using the truncated Wigner approximati…
Quantum coherence (QCh) is considered to be a key ingredient in quantum resource theories and also plays a pivotal role in the design and implementation of various information processing tasks. Consequently, it becomes important for us to create more number coherent quantum states between two labs from a given coherent state shared initially. We call this process as \textbf{Broadcasting of Quantum Coherence (QCh)}. In this work we extensively study the problem of broadcasting of QCh. In order to have a holistic view of broadcasting, we start with a most general representation two qubit mixed s…
Quantum resources, such as coherence, discord, and entanglement, play as a key role for demonstrating advantage in many computation and communication tasks. In order to find the nature behind these resources, tremendous efforts have been made to explore the connections between them. In this work, we extend the single party coherence resource framework to the distributed scenario and relate it to basis-dependent discord. We show the operational meaning of basis-dependent discord in quantum key distribution. By formulating a framework of basis-dependent discord, we connect these quantum resource…
We analyze the optimal basis for generating the maximum relative entropy of quantum coherence by an arbitrary gate on a two-qubit system. The optimal basis is not unique, and the high quantum coherence generating gates are also typically high entanglement generating ones and vice versa. However, the profile of the relative frequencies of Haar random unitaries generating different amounts of entanglement for a fixed amount of quantum coherence is different from the one in which the roles of entanglement and quantum coherence are reversed, although both follow the beta distribution.
Nitrogen-vacancy (NV) center in diamond is an ideal candidate for quantum sensors because of its excellent optical and coherence property. However, previous studies are usually conducted at low or room temperature. The lack of full knowledge of coherence properties of the NV center at high temperature limits NV's further applications. Here, we systematically explore the coherence properties of the NV center ensemble at temperatures from 300 K to 600 K. Coherence time $T_2$ decreases rapidly from $184 μs$ at 300 K to $30 μs$ at 600 K, which is attributed to the interaction with paramagnetic imp…
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this question completely for qubit states by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion where the process is enhanced by making use of correlations with a second party. Building on these…
The problem of optimal control of non-Markovian open quantum system via weak measurement is presented. Based on the non-Markovian master equation, we evaluate exactly the non-Markovian effect on the dynamics of the system of interest interacting with a dissipative reservoir. We find that the non-Markovian reservoir has dual effects on the system: dissipation and backaction. The dissipation exhausts the coherence of the quantum system, whereas the backaction revives it. Moreover, we design the control Hamiltonian with the control laws attained by the stochastic optimal control and the correspon…
We present an optimal probabilistic protocol to distill quantum coherence. Inspired by a specific entanglement distillation protocol, our main result yields a strictly incoherent operation that produces one of a family of maximally coherent states of variable dimension from any pure quantum state. We also expand this protocol to the case where it is possible, for some initial states, to avert any waste of resources as far as the output states are concerned, by exploiting an additional transformation into a suitable intermediate state. These results provide practical schemes for efficient quant…
Using on-demand coherence conversion via optical locking in conventional stimulated (three-pulse) photon echoes, ultralong, ultraefficient photon storage has been observed in a rare-earth Pr3+ doped Y2SiO5, where storage time is several orders of magnitude longer and retrieval efficiency is enhanced by fifty times. Compared with the same method applied to two-pulse photon echoes for a rephasing halt, use of spectral grating in the stimulated photon echoes offers a phase-independent coherence conversion between optical and spin states. Eventually an ultralong spin population decay-dependent pho…
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite systems. On this basis, we introduce a new measure of quantum coherence, the basis-free quantum coherence and prove that this quantity is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two…
The interaction between an atomic system and a few-cycle ultrafast pulse carries rich physics and a considerable application prospect in quantum-coherence control. However, theoretical understanding of its general behaviors has been hindered by the lack of an analytical description in this regime, especially with regard to the impact of the carrier-envelope phase (CEP). Here, we present an analytical theory that describes a two-level atom driven by a far-off-resonance, few-cycle square pulse. A simple, closed-form solution of the Schrodinger equation is obtained under the first-order perturbat…
The impacts of quantum coherence on nonequilibrium thermodynamics become observable by dividing the heat and work into the conventional diagonal part and the other part relaying on the superpositions and the time derivative of Hamiltonian. Specializing to exactly-solvable dynamics of Larmor precession, we build a quantum Otto heat engine employing magnetic-driven atomic rotations. The coherence induced by the population transition guarantees the positive work output when the control protocol is time dependent. The time-dependent control of a quantum heat engine implements the correspondence be…
Molecular Vibronic Complexity as a Quantum Resource for Optimal Control: Nonadiabatic Mixing Creates Protected Coherence Subspaces in Dissipative Environments
Theoretical and Computational Chemistry Institute, Heinrich-Heine-Universität Düsseldorf（杜塞尔多夫大学理论与计算化学研究所）
Light induced processes in nature occur by irradiation with slowly turned-on incoherent light. The general case of time-dependent incoherent excitation is solved here analytically for V-type systems using a newly developed master equation method. Clear evidence emerges for the disappearance of radiatively induced coherence as turn-on times of the radiation exceed characteristic system times. The latter is the case, in nature, for all relevant dynamical time scales for other than nearly degenerate energy levels. We estimate that, in the absence of non-radiative relaxation and decoherence, turn-…
Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase reduction theory recently developed for quantum nonlinear oscillators, two types of optimization problems, one for the stability and the other for the phase coherence of the entrained state, are considered. The optimal waveforms of the periodic amplitude modulation can be derived by applying the classical optimization methods to the semiclassical phase equation that approximately describes the quantum limit-cycle dynamics…
We study the steady-state characteristics and the transient behavior of the nonequilibrium double-dot Aharonov-Bohm interferometer using analytical tools and numerical simulations. Our simple setup includes noninteracting degenerate quantum dots that are coupled to two biased metallic leads at the same strength. A magnetic flux $Φ$ is piercing the setup perpendicularly. As we tune the degenerate dots energies away from the symmetric point we observe four nontrivial magnetic flux control effects: (i) flux dependency of the dots occupation, (ii) magnetic flux induced occupation difference betwee…
The atomistic resolution recently achieved by ultrafast spectroscopies demands corresponding theoretical advances. Real-time time-dependent density-functional theory (RT-TDDFT) with Ehrenfest dynamics offers an optimal trade-off between accuracy and computational costs to study electronic and vibrational dynamics of laser-excited materials in the sub-picosecond regime. However, this approach is unable to account for thermal effects or zero-point energies which are crucial in the physics involved. Herein, we adopt a quantum-semiclassical method based on RT-TDDFT+Ehrenfest to simulate laser-indu…
