A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to the diagonal elements of any observable jointly measurable with it, leading to a general criterion for the coherence needed for incompatibility. Specialising to the case where the second observable is incoherent (diagonal), we develop a concrete method for solving incompatibility problems, tractable even in large systems by analytical bounds, without resorting to numerical optimisation. We verify the consistency of our method by a quick proof of the known noise bound for mutually unbiased bases, and apply it to study emergent classicality in the spin-boson model of an N-qubit open quantum system. Finally, we formulate our theory in an operational resource-theoretic setting involving "genuinely incoherent operations" used previously in the literature, and show that if the coherence is insufficient to sustain incompatibility, the associated joint measurements have sequential implementations via incoherent instruments.
Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum coherence of two states as the coherence of one state in the reference basis spanned by the eigenvectors of another one and establish its quantitative connections with the extent of mutual incompatibility of two states. We also show that the proposed relative quantum coherence, which can take any form of measures such as $l_1$ norm and relative entropy, can b…
The well-known two-slit interference is understood as a special relation between observable (localization at the slits) and state (being on both slits). Relation between an observable and a quantum state is investigated in the general case. It is assumed that the amount of ceherence equals that of incompatibility between observable and state. On ground of this, an argument is peresented that leads to a natural quantum measure of coherence, called "coherence or incompatibility information". Its properties are studied in detail making use of 'the mixing property of relative entropy' derived in t…
We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is inconsequential, hence probability distribution of outcomes of any observable remains undisturbed. We define relative entropy of the two marginal probability distributions as a measure of quantumness in the state, which is revealed only in presence of two non-commuting observables. Like all other measures, we show that the proposed measure satisfies some basic axioms. A…
When observations must come from incompatible devices and cannot be produced by compatible devices? This question motivates two integer valued quantifications of incompatibility, called incompatibility dimension and compatibility dimension. The first one quantifies how many states are minimally needed to detect incompatibility if the test states are chosen carefully, whereas the second one quantifies how many states one may have to use if they are randomly chosen. With concrete examples we show that these quantities have unexpected behaviour with respect to noise.
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability distributions associated with different quantum measurements can be converted into one another by probabilistic post-processing. The induced preorder over quantum measurements is directly related to multivariate majorization and gives rise to families of monotones, i.e., scalar quantifiers that preserve the ordering. For the case of orthogonal measurement we e…
The existence of incompatible measurements is a fundamental phenomenon having no explanation in classical physics. Intuitively, one considers given measurements to be incompatible within a framework of a physical theory, if their simultaneous implementation on a single physical device is prohibited by the theory itself. In the mathematical language of quantum theory, measurements are described by POVMs (positive operator valued measures), and given POVMs are by definition incompatible if they cannot be obtained via coarse-graining from a single common POVM; this notion generalizes noncommutati…
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a…
We identify the simplest combinations of entanglement and incompatibility giving the maximum quantum violation for each of the 46 classes of tight Bell inequalities for the (3,2,2) scenario, i.e., three parties, two measurements per party, and two outcomes per measurement. This allows us to classify the maximum quantum nonlocality according to the simplest resources needed to achieve it. We show that entanglement and incompatibility only produce maximum nonlocality when they are combined in specific ways. For each entanglement class there is, in most cases, just one incompatibility class leadi…
In relation of observable and quantum state, the entity $I_C$ from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this article its application to quantum correlations in bipartite states is studied. It is shown that Zurek's quantum discord can always be expressed as excess coherence information (global minus local). Strong and weak zero-discord cases are distinguished and investigated in terms of necessary and sufficient and sufficient conditions respectively. A unique string of relevant subsystem observables, each a function of the next, for "interrogat…
Quantum Estimation under Decoherence in Neutrino Oscillations: Quantum Resources, Flavor Accessibility, and Multiparameter Incompatibility
LPMS, Faculty of Sciences, Ibn Tofail University（伊本·图费利大学理学院）；LPHE–Modeling and Simulation, Faculty of Sciences, Mohammed V University in Rabat（拉巴特穆罕默德五世大学理学院）；Centre of Physics and Mathematics, CPM, Faculty of Sciences, Mohammed V University in Rabat（拉巴特穆罕默德五世大学理学院物理与数学中心）；College of Computing and Mathematical Sciences, Department of Applied Mathematics and Sciences and Center for Cyber-Physical Systems (C2PS), Khalifa University of Science and Technology（阿联酋哈利法大学科学技术学院计算与数理科学学院）
Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We app…
Manipulation and quantification of quantum resources are fundamental problems in quantum physics. In the asymptotic limit, coherence distillation and dilution have been proposed by manipulating infinite identical copies of states. In the non-asymptotic setting, finite data-size effects emerge, and the practically relevant problem of coherence manipulation using finite resources has been left open. This letter establishes the one-shot theory of coherence dilution, which involves converting maximally coherent states into an arbitrary quantum state using maximally incoherent operations, dephasing…
Quantum coherence and quantum entanglement represent two fundamental features of non-classical systems that can each be characterized within an operational resource theory. In this paper, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a g…
Having the quantum correlations in a general bipartite state in mind, the information accessible by simultaneous measurement on both subsystems is shown never to exceed the information accessible by measurement on one subsystem, which, in turn is proved not to exceed the von Neumann mutual information. A particular pair of (opposite- subsystem) observables are shown to be responsible both for the amount of quasi-classical correlations and for that of the purely quantum entanglement in the pure-state case: the former via simultaneous subsystem measurements, and the latter through the entropy of…
One of the central features of quantum theory is that there are pairs of quantum observables that cannot be measured simultaneously. This incompatibility of quantum observables is a necessary ingredient in several quantum phenomena, such as measurement uncertainty relations, violation of Bell inequalities and steering. Two quantum observables that admit a simultaneous measurement are, in this respect, classical. A finer classification of classicality can be made by formulating four symmetric relations on the set of observables that are stronger than compatibility; they are broadcastability, on…
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…
Optical coherence tomography has become an important imaging technology in cardiology and ophthalmology, with other applications under investigations. Major advances in optical coherence tomography (OCT) imaging are likely to occur through a quantum field approach to the technology. In this paper, which is the first part in a series on the topic, the quantum basis of OCT first order correlations is expressed in terms of full field quantization. Specifically first order correlations are treated as the linear sum of single photon interferences along indistinguishable paths. Photons and the elect…
We explore the role of quantum fluctuations in the strong-coupling limit of the dissipative Jaynes-Cummings oscillator driven on resonance. For weak excitation, we derive analytical expressions for the spectrum and the intensity correlation function for the photons scattered by the two-state atom coupled to the coherently driven cavity mode. We do so by writing down a birth-death process adding the higher orders in the excitation strength needed to go beyond the pure-state factorization, following the method introduced in [H. J. Carmichael, {\it Statistical Methods in Quantum Optics 2}, Spring…
Jianghan University（江汉大学）；North Carolina State University（北卡罗来纳州立大学）；Central China Normal University（华中师范大学）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局（A*STAR））
We make a thorough study of the spreading of quantum coherence (QC), as quantified by the $l_{1}$-norm QC, when a qubit (a two-level quantum system) is subjected to noise quantum channels commonly appearing in quantum information science. We notice that QC is generally not conserved and that even incoherent initial states can lead to transitory system-environment QC. We show that for the amplitude damping channel the evolved total QC can be written as the sum of local and non-local parts, with the last one being equal to entanglement. On the other hand, for the phase damping channel (PDC) enta…
The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint poin…
We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the cluster state needed for the computation and its consumption by measurements are carried out simultaneously. As a consequence, effective clusters of one spatial dimension fewer than in the standard approach are sufficient for computation. In particular, universal computation requires only a one-dimensional array of memories. The scheme applies to discrete-v…
Knowing a quantum system's environment is critical for its practical use as a quantum device. Qubit sensors can reconstruct the noise spectral density of a classical bath, provided long enough coherence time. Here we present a protocol that can unravel the characteristics of a more complex environment, comprising both unknown coherently coupled quantum systems, and a larger quantum bath that can be modeled as a classical stochastic field. We exploit the rich environment of a Nitrogen-Vacancy center in diamond, tuning the environment behavior with a bias magnetic field, to experimentally demons…
Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hardware for implementing quantum information and computing protocols in scalable systems. Nevertheless, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times that are generally longer than the coherence time of the electron spin. Here, we demonstrate a scheme for circumventing this problem by indirect control: We apply a small number of short pulses only to the …
We compute on all quantum states several measures that characterise asymptotic quantum coherence manipulation under restricted classes of operations. We focus on the distillable coherence, i.e. the maximum rate of production of approximate pure bits of coherence starting from independent copies of an input state $ρ$, and on the coherence cost, i.e. the minimum rate of consumption of pure coherence bits that is needed to generate many copies of $ρ$ with vanishing error. We obtain the first closed-form expression for the distillable coherence under strictly incoherent operations (SIO), proving t…
Incompatibility of certain measurements -- impossibility of obtaining deterministic outcomes simultaneously -- is a well known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to device dependent QKD protocols. Typically, in these applications the measurements are chosen from a predetermined set based on a classical random variable. One can naturally ask, whether the non-determinism of the outcomes is due to intrinsic hiding property of quantum mechanics, or rather by the fact that classical, incoherent information entered the system …
During the long course of evolution, nature has learnt how to exploit quantum effects. In fact, recent experiments reveal the existence of quantum processes whose coherence extends over unexpectedly long time and space ranges. In particular, photosynthetic processes in light-harvesting complexes display a typical oscillatory dynamics ascribed to quantum coherence. Here, we consider the simple model where a dimer made of two chromophores is strongly coupled with a quasi-resonant vibrational mode. We observe the occurrence of wide oscillations of genuine quantum correlations, between electronic …
Materials for Quantum Information Science: Roles in the Quantum Evolution 2.0
Virginia Tech（弗吉尼亚理工大学）；Virginia Tech National Security Institute（弗吉尼亚理工学院国家安全研究所）；Northwestern University（西北大学）；University of Maryland, College Park（马里兰大学帕克分校）
The non-commutativity of position and momentum observables is a hallmark feature of quantum physics. However this incompatibility does not extend to observables which are periodic in these base variables. Such modular-variable observables have been suggested as tools for fault-tolerant quantum computing and enhanced quantum sensing. Here we implement sequential measurements of modular variables in the oscillatory motion of a single trapped ion, using state-dependent displacements and a heralded non-destructive readout. We investigate the commutative nature of modular variable observables by de…
In the framework of quantum thermodynamics preparing a quantum system in a general state requires the consumption of two distinct resources, namely, work and coherence. It has been shown that the work cost of preparing a quantum state is determined by its free energy. Considering a similar setting, here we determine the coherence cost of preparing a general state when there are no restrictions on work consumption. More precisely, the coherence cost is defined as the minimum rate of consumption of systems in a pure coherent state, that is needed to prepare copies of the desired system. We show …
Lightwave periodic driving of nearly dissipation-less currents has recently emerged as a universal control concept for both superconducting (SC) and topological electronics applications. While exciting progress has been made towards THz-driven superconductivity, our understanding of the interactions able to drive non-equilibrium pairing is still limited, partially due to the lack of direct measurements of high-order correlation functions. Such measurements would exceed conventional single-particle spectroscopies and perturbative responses to fully characterize quantum states far-from-equilibri…
Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine's working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or he…
Sensitive magnetometers that can operate in high magnetic fields are essential for detecting magnetic resonance signals originating from small ensembles of quantum spins. Such devices have potential applications in quantum technologies, in particular quantum computing. We present a novel experimental setup implementing a differential flux measurement using two DC-SQUID magnetometers. The differential measurement allows for cancellation of background flux signals while enhancing sample signal. The developed protocol uses pulsed readout which minimizes on-chip heating since sub-Kelvin temperatur…
Qubits made from superconducting materials are a mature platform for quantum information science application such as quantum computing. However, materials-based losses are now a limiting factor in reaching the coherence times needed for applications. In particular, knowledge of the atomistic structure and properties of the circuit materials is needed to identify, understand, and mitigate materials-based decoherence channels. In this work we characterize the atomic structure of the native oxide film formed on Nb resonators by comparing fluctuation electron microscopy experiments to density func…
Nonlocal advantage of quantum coherence in tau-lepton pairs from electron--positron collisions
Enrico Fermi Institute, University of Chicago（芝加哥大学恩里科·费米研究所）；Instituto de Estructura de la Materia, IEM-CSIC（材料结构研究所（CSIC））；Indian Institute of Technology Jodhpur（印度理工学院乔德普尔分校）；Department of Physics, University of British Columbia（不列颠哥伦比亚大学物理系）；TRIUMF（特利昂夫实验室）
