We plot the geometry of several distance-based quantifiers of coherence for Bell-diagonal states. We find that along with both $l_{1}$ norm and relative entropy of coherence changes continuously from zero to one, their surfaces move from the separable regions to the entangled regions. Based on this fact, it is more illuminating to use an intuitive geometry to explain quantum states with nonzero coherence can be used for entanglement creation, rather than the other way around. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equal to its relative entropy of coherence and depict the surfaces of the equality. We give surfaces of relative entropy of coherence for $X$ states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherence under local nondissipative channels decrease.
Quantum coherence and entanglement orignate from the superposition principle. We derive a rigorous relation between the ${l_1}$-norm of coherence and concurrence, in that we show that the former is always greater than the latter. This result highlights the hierarchical relationship between coherence and concurrence, and proves coherence to be a fundamental and ubiquitous resource. We derive an analogous form of monogamy inequality which is based on the partial coherence of the reduced two-qubit and reduced single qubit of the particular class of three-qubit state. Moreover, we provide coherenc…
The influence of the initial preparation on dephasing in open quantum dynamics is studied using an exactly solvable model of a two-level system (qubit) interacting with a bosonic bath. It is found that for some classes of non-selective preparation measurements, qubit-bath correlations lead to a significant enhancement of coherence in the qubit at the initial stage of evolution. The time behavior of the qubit purity and entropy in the regime of enhancement of coherence is considered for different temperatures and coupling strengths.
Recently, a basis-invariant measure of coherence known as the intrinsic degree of coherence has been established for classical and single-particle quantum states [JOSA B {\bf 36}, 2765 (2019)]. Using the same mathematical construction, in this article, we define the intrinsic degree of coherence of two-qubit states and demonstrate its usefulness in quantifying two-particle quantum correlations and entanglement. In this context, first of all, we show that the intrinsic degree of coherence of a two-qubit state puts an upper bound on the violations of Bell inequalities that can be achieved with t…
We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO $\subset$ PIO $\subset$ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been pr…
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 interconversion of this resource. Here we solve this question completely for mixed states of qubits by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. This implies new lower bounds on the asymptotic state conversion rate between mixed single-qubit states which in some cases is proven to be tight. Furthermore, we obtain the minimal distillable coherence for given…
We propose scalable architectures for the coherence-preserving qubits introduced by Bacon, Brown, and Whaley [Phys. Rev. Lett. {\bf 87}, 247902 (2001)]. These architectures employ extra qubits providing additional degrees of freedom to the system. We show that these extra degrees of freedom can be used to counter errors in coupling strength within the coherence-preserving qubit and to combat interactions with environmental qubits. The presented architectures incorporate experimentally viable methods for inter-logical-qubit coupling and can implement a controlled phase gate via three simultaneo…
In this paper, we investigate preservation of quantum coherence of a single-qubit interacting with a zero-temperature thermal reservoir through the addition of noninteracting qubits in the reservoir. Moreover, we extend this scheme to preserve quantum entanglement between two and three distant qubits, each of which interacts with a dissipative reservoir independently. At the long time limit, we obtained analytical expressions for the coherence measure and the concurrence of two and three qubits in terms of the number of additional qubits. It is observed that, by increasing the number of additi…
Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound $L$ of $l_{1}$ norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound $U$ of $l_{1}$ norm of coherence of separable…
We investigate the dynamics of coherence and entanglement of vibrating qubits. Firstly, we consider a single trapped ion qubit inside a perfect cavity and successively we use it to construct a bipartite system made of two of such subsystems, taken identical and noninteracting. As a general result, we find that qubit vibration can lead to prolonging initial coherence in both single-qubit and two-qubit system. However, despite of this coherence preservation, we show that the decay of the entanglement between the two qubits is sped up by the vibrational motion of the qubits. Furthermore, we highl…
We demonstrate sympathetic cooling of a 43Ca+ trapped-ion "memory" qubit by a 40Ca+ "coolant" ion near the ground state of both axial motional modes, whilst maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during 10 cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is O(0.01%) infidelity per cooling cycl…
We study the influence of an external driving field on the coherence properties of a qubit under the influence of bit-flip noise. In the presence of driving, two paradigmatic cases are considered: (i) a field that results for a suitable choice of the parameters in so-called coherent destruction of tunneling and (ii) one that commutes with the static qubit Hamiltonian. In each case, we give for high-frequency driving a lower bound for the coherence time. This reveals the conditions under which the external fields can be used for coherence stabilization.
We study the interplay between coherence trapping, information back-flow and the form of the reservoir spectral density for dephasing qubits. We show that stationary coherence is maximized when the qubit undergoes non-Markovian dynamics, and we elucidate the different roles played by the low and high frequency parts of the environmental spectrum. We show that the low frequencies fully determine the presence or absence of information back-flow while the high frequencies dictate the maximal amount of coherence trapping.
The effects of the measurement apparatus on quantum coherence are studied by considering a purely dephasing model of a qubit. The initial state is prepared from a thermal state of the whole system by performing a nonselective measurement on the qubit. The magnitude of the initial postmeasurement coherence is bounded by the value $1/2$, which is realized with special measurement schemes and in the low-temperature limit. The magnitude of coherence identically vanishes, increases or decreases with approximately constant velocity over a determined short time scale, according to the choice of the p…
We study the coherence trapping of a qubit correlated initially with a non-Markovian bath in a pure dephasing channel. By considering the initial qubit-bath correlation and the bath spectral density, we find that the initial qubit-bath correlation can lead to a more efficient coherence trapping than that of the initially separable qubit-bath state. The stationary coherence in the long time limit can be maximized by optimizing the parameters of the initially correlated qubit-bath state and the bath spectral density. In addition, the effects of this initial correlation on the maximal evolution s…
Using the axiomatic definition of the coherence measure, such as the $l_{1}$ norm and the relative entropy, we study the phenomena of two-qubit system quantum coherence through quantum channels where successive uses of the channels are memory. Different types of noisy channels with memory, such as amplitude damping, phase-damping, and depolarizing channels effect on quantum coherence have been discussed in detail. The results show that, quantum channels with memory can efficiently protect coherence from noisy channels. Particularly, as channels with perfect memory, quantum coherence is unaffec…
We consider the problem of stabilizing the coherence of a single qubit subject to Markovian decoherence, via the application of a control Hamiltonian, without any additional resources. In this case neither quantum error correction/avoidance, nor dynamical decoupling applies. We show that using tracking-control, i.e., the conditioning of the control field on the state of the qubit, it is possible to maintain coherence for finite time durations, until the control field diverges.
We show how the dispersive regime of the Jaynes-Cummings model may serve as a valuable tool to the study of open quantum systems. We employ it in a bottom-up approach to build an environment that preserves qubit energy and induces varied coherence dynamics. We then present the derivation of a compact expression for the qubit coherence, applied here to the case of a finite number of thermally populated modes in the environment. We also discuss how the model parameters can be adjusted to facilitate the production of short-time monotonic decay (STMD) of the qubit coherence. Our results provide a …
Entanglement is a purely quantum mechanical phenomenon and thus it has no classical analog. On the other hand, coherence is a well-known phenomenon in classical optics and in quantum mechanics. Recent research shows that quantum coherence may act as a useful resource in quantum information theory. We will employ here quantum coherence to detect and classify the entanglement property of three-qubit states. Moreover, we have shown that if any three-qubit state violates another necessary condition for the detection of a general biseparable state then the given three-qubit state cannot be a bisepa…
We report a superconducting artificial atom with an observed quantum coherence time of T2*=95us and energy relaxation time T1=70us. The system consists of a single Josephson junction transmon qubit embedded in an otherwise empty copper waveguide cavity whose lowest eigenmode is dispersively coupled to the qubit transition. We attribute the factor of four increase in the coherence quality factor relative to previous reports to device modifications aimed at reducing qubit dephasing from residual cavity photons. This simple device holds great promise as a robust and easily produced artificial qua…
The identification of spacial noise correlation is of critical importance in developing error-corrected quantum devices, but it has barely been studied so far. In this work, we utilize an effective new method called qubit motion, to efficiently determine the noise correlations between any pair of qubits in a 7-qubit superconducting quantum system. The noise correlations between the same pairs of qubits are also investigated when the qubits are at distinct operating frequencies. What's more, in this multi-qubit system with the presence of noise correlations, we demonstrate the enhancing effect …
I present a general scheme through which the evidence of a superposition involving distinct classical-like states of a macroscopic system can be probed. The scheme relies on a qubit being coupled to a macroscopic harmonic oscillator in such a way that it can be used to both prepare and probe a macroscopic superposition. Two potentially realizable implementations, one with a flux qubit coupled to a LC circuit, and the other with an ion-trap qubit coupled to the collective motion of several ions, are proposed.
We report the creation of Greenberger-Horne-Zeilinger states with up to 14 qubits. By investigating the coherence of up to 8 ions over time, we observe a decay proportional to the square of the number of qubits. The observed decay agrees with a theoretical model which assumes a system affected by correlated, Gaussian phase noise. This model holds for the majority of current experimental systems developed towards quantum computation and quantum metrology.
Coherence and entanglement are the two most crucial resources for various quantum information processing tasks. Here, we study the interplay of coherence and entanglement under the action of different three qubit quantum cloning operations. Considering certain well-known quantum cloning machines (input state independent and dependent), we provide examples of coherent and incoherent operations performed by them. We show that both the output entanglement and coherence could vanish under incoherent cloning operations. Coherent cloning operations on the other hand, could be used to construct a uni…
Quantum coherence, the ability of a quantum system to be in a superposition of orthogonal quantum states, is a distinct feature of the quantum mechanics, thus marking a deviation from classical physics. Coherence finds its applications in quantum sensing and metrology, quantum thermodynamics and computation. A particularly interesting is the possibility to observe coherence arising in counter-intuitive way from thermal energy that is without implementation of intricate protocols involving coherent driving sequences. In this manuscript, we investigate quantum coherence emerging in a hybrid syst…
Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coh…
Two-level ionic systems, where quantum information is encoded in long lived states (qubits), are discussed extensively for quantum information processing. We present a collection of measurements which characterize the stability of a qubit based on the $S_{1/2}$--$D_{5/2}$ transition of single $^{40}$Ca$^+$ ions in a linear Paul trap. We find coherence times of $\simeq$1 ms, discuss the main technical limitations and outline possible improvements.
In this paper, we analyze the evolution of quantum coherence in a two-qubit system going through the amplitude damping channel. After they have gone through this channel many times, we analyze the systems with respect to the coherence of their output states. When only one subsystem goes through the channel, frozen coherence occurs if and only if this subsystem is incoherent and an auxiliary condition is satisfied for the other subsystem. When two subsystems go through this quantum channel, quantum coherence can be frozen if and only if the two subsystems are both incoherent. We also investigat…
It is shown that quantum coherence is conserved in a principal system in the case that the system is coupled to a fast dissipating environment [arXiv:0709.0562]. The phenomenon is called the quantum wipe effect. Here, this effect is reviewed and the analytical proof for a model system consisting of a one-qubit system coupled to a fast dissipating environment is extended to an environment at a thermal equilibrium.
Decoherence, resulting from unwanted interaction between a qubit and its environment, poses a serious challenge towards the development of quantum technologies. Recently, researchers have started analysing how real-time Hamiltonian learning approaches, based on estimating the qubit state faster than the environmental fluctuations, can be used to counteract decoherence. In this work, we investigate how the back-action of the quantum measurements used in the learning process can be harnessed to extend qubit coherence. We propose an adaptive protocol that, by learning the qubit environment, narro…
Do experiments based on superconducting loops segmented with Josephson junctions (e.g., flux qubits) show macroscopic quantum behavior in the sense of Schrödinger's cat example? Various arguments based on microscopic and phenomenological models were recently adduced in this debate. We approach this problem by adapting (to flux qubits) the framework of large-scale quantum coherence, which was already successfully applied to spin ensembles and photonic systems. We show that contemporary experiments might show quantum coherence more than 100 times larger than experiments in the classical regime. …
Optically addressable spins are a promising platform for quantum information science due to their combination of a long-lived qubit with a spin-optical interface for external qubit control and read out. The ability to chemically synthesize such systems - to generate optically addressable molecular spins - offers a modular qubit architecture which can be transported across different environments, and atomistically tailored for targeted applications through bottom-up design and synthesis. Here we demonstrate how the spin coherence in such optically addressable molecular qubits can be controlled …
Kitaev's 0-$π$ qubit encodes quantum information in two protected, near-degenerate states of a superconducting quantum circuit. In a recent work, we have shown that the coherence times of a realistic 0-$π$ device can surpass that of today's best superconducting qubits [Groszkowski et al., New Journal of Physics 20 043053 (2018)]. Here we address controllability of the 0-$π$ qubit. Specifically, we investigate the potential for dispersive control and readout, and introduce a new, fast and high-fidelity single-qubit gate that can interpolate smoothly between logical X and Z. We characterize the …
We investigate analytically and numerically the steady-state entanglement and coherence of two coupled qubits each interacting with a local boson or fermion reservoir, based on the Bloch-Redfield master equation beyond the secular approximation. We find that there is non-vanishing steady-state coherence in the nonequilibrium scenario, which grows monotonically with the nonequilibrium condition quantified by the temperature difference or chemical potential difference of the two baths. The steady-state entanglement in general is a non-monotonic function of the nonequilibrium condition as well as…
We report on the coherence of Greenberger-Horne-Zeilinger (GHZ) states comprised of up to 8 qubits in the IBM ibmqx5 16-qubit quantum processor. In particular, we evaluate the coherence of GHZ states with $N=1,\ldots,8$ qubits, as a function of a delay time between state creation and measurement. We find that the decay in coherence occurs at a rate that is linear in the number of qubits. This is consistent with a model in which the dominant noise affecting the system is uncorrelated across qubits.
When quantum systems interact with the environment they lose their quantum properties, such as coherence. Quantum erasure makes it possible to restore coherence in a system by measuring its environment, but accessing the whole of it may be prohibitive: realistically one might have to concentrate only on an accessible subspace and neglect the rest. If that is the case, how good is quantum erasure? In this work we compute the largest coherence $\langle \mathcal C\rangle$ that we can expect to recover in a qubit, as a function of the dimension of the accessible and of the inaccessible subspaces o…
Superconducting circuits rank among the most interesting architectures for the implementation of quantum information processing devices. The recently proposed 0-$π$ qubit [Brooks et al., Phys. Rev. A ${\bf 87}$, 52306 (2013)] promises increased protection from spontaneous relaxation and dephasing. In practice, this ideal behavior is only realized if the parameter dispersion among nominally identical circuit elements vanishes. In this paper we present a theoretical study of the more realistic scenario of slight variations in circuit elements. We discuss how the coupling to a spurious, low-energ…
The unavoidable effect of the environmental noise due to nuclear spins and charge traps is included in the study of the hybrid qubit dynamics. Hybrid qubit dues its name to the advantageous combination of manipulation speed of a charge qubit with the longevity of a spin qubit. It consists of three electrons confined through external gate voltages in a double quantum dot and deserves special interest in quantum computation applications due to its advantages in terms of fabrication, control and only electrical manipulation. Hybrid qubit is protected against global magnetic fluctuations since it …
In this paper, we study the ordering states with Tsallis relative $α$-entropies of coherence and $l_{1}$ norm of coherence for single-qubit states. We show that any Tsallis relative $α$-entropies of coherence and $l_{1}$ norm of coherence give the same ordering for single-qubit pure states. However, they don't generate the same ordering for some high dimensional pure states, even though these states are pure. We also consider three special Tsallis relative $α$-entropies of coherence, such as $C_{1}$ ,$C_{2}$ and $C_{\frac{1}{2}}$, and show any one of these three measures and $C_{l_{1}}$ will n…
For neutral atom qubits, the two-qubit gate is typically realized via the Rydberg blockade effect, which hints about the special status of the Rydberg level besides the regular qubit register states. Here, we carry out experimental and theoretical studies to reveal how the ground-Rydberg coherence of the control qubit atom affects the process of two-qubit Controlled-Z ($C_Z$) gate, such as the commonly used ground-Rydberg $π$-gap-$π$ pulse sequence originally proposed in Phys. Rev. Lett. \textbf{85}, 2208 (2000). We measure the decoherence of the control qubit atom after the $π$-gap-$π$ pulses…
We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength $g_2$. The coherence decays and revives at a period $2π/g_2$, with the width of coherence peak decreases as the temperature increases, hence providing a way to measure $g_2$ precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in…
Realizing a long coherence time quantum memory is a major challenge of current quantum technology. Here, we report a single \Yb ion-qubit memory with over one hour coherence time, an order of improvement compared to the state-of-the-art record. The long coherence time memory is realized by addressing various technical challenges such as ambient magnetic-field noise, phase noise and leakage of the microwave oscillator. Moreover, systematically study the decoherence process of our quantum memory by quantum process tomography, which enables to apply the strict criteria of quantum coherence, relat…
Beyond-Ten-Hour Coherence in a Decoherence-Free Trapped-Ion Clock Qubit
Tsinghua University（清华大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Hefei National Laboratory（合肥国家实验室）；Renmin University of China（中国人民大学）
Quantum coherence and quantum correlations are studied in the strongly interacting system composed of two qubits and an oscillator with the presence of a parametric medium. To analytically solve the system, we employ the adiabatic approximation approach. It assumes each qubit's characteristic frequency is substantially lower than the oscillator frequency. To validate our approximation, a good agreement between the calculated energy spectrum of the Hamiltonian with its numerical result is presented. The time evolution of the reduced density matrices of the two-qubit and the oscillator subsystem…
The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad frequency tunability, strong anharmonicity, high reproducibility, and relaxation times in excess of $40\,μ$s at its flux-insensitive point. Qubit relaxation times $T_1$ across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise, and 1/f flux noise, a noise source previously considered primarily in…
We study the relations between quantum coherence and quantum nonlocality, genuine quantum entanglement and genuine quantum nonlocality. We show that the coherence of a qubit state can be converted to the nonlocality of two-qubit states via incoherent operations. The results are also generalized to qudit case. Furthermore, rigorous relations between the quantum coherence of a single-partite state and the genuine multipartite quantum entanglement, as well as the genuine three-qubit quantum nonlocality are established.
Modern quantum technologies rely crucially on techniques to mitigate quantum decoherence; these techniques can be either passive, achieved for example via materials engineering, or active, typically achieved via pulsed monochromatic driving fields applied to the qubit. Using a solid-state defect spin coupled to a microwave-driven spin bath, we experimentally demonstrate a decoherence mitigation method based on spectral engineering of the environmental noise with a polychromatic drive waveform, and show that it outperforms monochromatic techniques. Results are in agreement with quantitative mod…
Superconducting circuits are a leading platform for quantum computing. However, their coherence times are still limited and exhibit temporal fluctuations. Those phenomena are often attributed to the coupling between qubits and material defects that can be well described as an ensemble of two-level systems (TLSs). Among them, charge fluctuators inside amorphous oxide layers contribute to both low-frequency $1/f$ charge noise and high-frequency dielectric loss, causing fast qubit dephasing and relaxation. Moreover, spectral diffusion from mutual TLS interactions varies the noise amplitude over t…
The long-lived, efficient storage and retrieval of a qubit encoded on a photon is an important ingredient for future quantum networks. Although systems with intrinsically long coherence times have been demonstrated, the combination with an efficient light-matter interface remains an outstanding challenge. In fact, the coherence times of memories for photonic qubits are currently limited to a few milliseconds. Here we report on a qubit memory based on a single atom coupled to a high-finesse optical resonator. By mapping and remapping the qubit between a basis used for light-matter interfacing a…
We discuss how the observation of population localization effects in periodically driven systems can be used to quantify the presence of quantum coherence in interacting qubit arrays. Essential for our proposal is the fact that these localization effects persist beyond tight-binding Hamiltonian models. This result is of special practical relevance in those situations where direct system probing using tomographic schemes becomes infeasible beyond a very small number of qubits. As a proof of principle, we study analytically a Hamiltonian system consisting of a chain of superconducting flux qubit…
