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 of its environment. We then imagine the following game: we are given a uniformly random pure state of $n+1$ qubits and we are asked to compute the largest coherence that we can retrieve on one of them by optimally measuring a certain number $0\leq a\leq n$ of the others. We find a surprising effect around the value $a\approx n/2$: the recoverable coherence sharply transitions between 0 and 1, indicating that in order to restore full coherence on a qubit we need access to only half of its physical environment (or in terms of degrees of freedom to just the square root of them). Moreover, we find that the recoverable coherence becomes a typical property of the whole ensemble as $n$ grows.
We show that conditional measurements on atoms following their interaction with a resonant cavity field mode can be used to effectively counter the decoherence of Fock-state superpositions due to cavity leakage.
We present a feasible scheme for reconstructing the quantum state of a field prepared inside a lossy cavity. Quantum coherences are normally destroyed by dissipation, but we show that at zero temperature we are able to retrieve enough information about the initial state, making possible to recover its Wigner function as well as other quasiprobabilities. We provide a numerical simulation of a Schroedinger cat state reconstruction.
A quantitative measure of quantum coherence was recently introduced, in the context of quantum information theory. This measure has also been propounded as a good quantifier of the wave nature of quantum objects. However, actually measuring coherence in an experiment is still considered a challenge. A procedure for measuring coherence in a multi-slit interference is proposed here. It can be used for experimentally testing duality relations for interference experiments involving more than two slits.
We examined the possibility of recovering the losses of entanglement and the non-local advantage by using the local symmetric operations. The improvement efficiency may be increased by applying the symmetric operations on both qubits. The recovering process of both phenomenon is exhibited clearly when only one qubit is accelerated and the symmetric operations is applied on both qubits. It is shown that, for large acceleration, the non-local coherent advantage may be re-birthed by using these symmetric operations.
Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113}, 140401 (2014)] presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure fulfills all the requirements dictated by the resource theory of quantum coherence measur…
A scheme is discussed for measuring Nth-order coherences of two orthogonally polarized light fields in a single spatial mode at very limited experimental cost. To implement the scheme, the only measurements needed are the Nth-order intensity moments after the light beam has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific settings of the wave plates. It is shown that this method can be applied for arbitrarily large N. A set of explicit values is given for the settings of the wave plates, constituting an optimal measurement of the Nth-orde…
The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on the implementation of its complementary concept, coherence from quantum measurements. By devising an accessible criterion which holds true in any classical statistical theory, we demonstrate that noncommutative quantum measurements violate this constraint, rendering it possible to perform an operational assessment of the measurement-based quantum coherence. In…
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 …
Direct access to the initial polarization of ${}^{13}C$ nuclei by measuring coherence evolution of an nitrogen-vacancy center spin qubit
Institute of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology（弗罗茨瓦夫科技大学基础技术学院理论物理研究所）；FZU - Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）
Measuring quantum states provides means to generate genuine random numbers. It has been shown that genuine randomness can be obtained even with an uncharacterized quantum source. In this work, we propose a framework that formalizes the idea of realizing source-independent quantum random number generation via measuring coherence. Without full state tomography, the coherence of the source can be estimated by coherence witnesses. The existing uncertainty-relation-based schemes can be treated as special cases under the coherence framework, as we design a nonlinear coherence witness that can essent…
One of the important goals of present research is to control and manipulate coherence in a broad variety of systems, such as semiconductor spintronics, biological photosynthetic systems, superconducting qubits and complex atomic networks. Over the past decades interferometry of atoms and molecules has proven to be a powerful tool to explore coherence. Here we demonstrate a near-field interferometer based on the Talbot effect, which allows to measure finite-range phase coherence of ultracold atoms in an optical lattice. We apply this interferometer to study the build-up of phase coherence after…
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. We explore the ability of adaptive optics to compensate for this disturbance by measuring and correcting cumulative phase shifts in the wavefront. These shifts can be represented as a sum of Zernike functions; we analyze the residual errors after correcting up to a certain number of Zernike modes when an orbital angular momentum state is transmitted through a turbulent atmosphere whose density fluctuations have a Kolmogorov s…
It has been proposed that measurement in quantum mechanics results from spontaneous breaking of a symmetry of the measuring apparatus and could be a unitary process that preserves coherence. Viewed in this manner, it is argued, non-destructive measurements should preserve this coherence and be reversible. It is shown that experiments with maximally entangled bipartite states can indeed distinguish between projective and unitary measurements.
Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. [PRL 113:140401 (2014)], following Åberg [arXiv:quant-ph/0612146], have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here i…
Optical low-coherence reflectometry is capable of unambiguously measuring positions of stacked, partially reflective layers in a sample object. It relies on the low coherence of the light source and the absolute distances are obtained from the position reading of a mechanical motor stage. We show how to exploit the simultaneous high and low coherence properties of energy-time entangled photon pairs to directly calibrates the position scale of an OLCR scan with a reference laser wavelength. In experiment, a precision of 1.6\,nm and good linearity is demonstrated.
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.
Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum system. In this paper, we put forward a notion of localizable coherence as the coherence that can be stored in a particular subsystem, either by measuring or just by disregarding the rest. We examine its spreading, its average properties in the Hilbert space and show that it can be applied to reveal the real-space structure of states of interest in quantum many-…
A technique complementary to those for spectral lines is proposed for the observation of continuum radiation. As, quantum mechanically, the radiation is a mixture of pure states, it should be possible to measure the temporal coherence of the states as a function of energy. We propose here experiments with just this possibility, showing the empirical grounds on which it is based. A simple means of measuring temporal coherence is with the extent of the interference pattern produced in a Young's double-slit experiment. Thus, we propose the use of such an experiment, but with a screen of energy me…
The problem of automatically protecting a quantum system against noise in a closed circuit is analyzed. A general scheme is developed built from two steps. At first, a distillation step is induced in which undesired components are removed to another degree of freedom of the system. Later a recovering step is employed which the system gains back its initial density. An Optimal-Control method is used to generate the distilling operator. The scheme is demonstrated by a simulation of a two level byte influenced by white noise. Undesired deviations from the target were shown to be reduced by at lea…
Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of coherence as an operational resource are still very limited. Here we show that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. This finding allows us to define a novel general class of measures of coherence for a quantum system of arbitrary dimension, in terms of the maximum bipartite …
Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum resource theory. Here, we introduce feasible methods to detect and estimate the coherence by constructing coherence witnesses for any finite-dimensional states. Our coherence witnesses detect coherent states by testing whether the expectation value of the witness is negative or not. Two typical coherence witnesses are proposed and discussed based on our witness…
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…
We experimentally demonstrate a bright pulsed source of correlated photon pairs at 1550 nm telecom band by pumping 300 m dispersion shifted fiber with a 4 ps pulse train. We investigate the coherence property of the source by measuring the second order intensity correlation function $g^{(2)}$ of individual signal (idler) photons. A preliminary Hong-Ou-Mandel type two-photon interference experiment with two such sources confirms the high temporal and spatial coherence of the source. The source is suitable for multi-photon quantum interference of independent sources, required in quantum informat…
We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided and sufficient conditions for the saturation of the upper bound are shown. These sufficient conditions always hold for two and three dimensional systems. This provides a tool to estimate the average coherence experimentally by measuring only the diagonal elements, which remarkably requires less measurements compared with state tomography. We then describe the pure state decompositions of qubit state in Bloch sphere geometrically. For an…
Quantification of coherence lies at the heart of quantum information processing and fundamental physics. Exact evaluation of coherence measures generally needs a full reconstruction of the density matrix, which becomes intractable for large-scale multipartite systems. Here, we propose a systematic theoretical approach to efficiently estimating lower and upper bounds of coherence in multipartite states. Under the stabilizer formalism, the lower bound is determined by the spectrum estimation method with a small number of measurements and the upper bound is determined by a single measurement. We …
A heavy hole confined to an InGaAs quantum dot promises the union of a stable spin and optical coherence to form a near perfect, high-bandwidth spin-photon interface. Despite theoretical predictions and encouraging preliminary measurements, the dynamic processes determining the coherence of the hole spin are yet to be understood. Here, we establish the regimes that allow for a highly coherent hole spin in these systems, recovering a crossover from hyperfine to electrical-noise dominated decoherence with a few-Tesla external magnetic field. Dynamical decoupling allows us to reach the longest gr…
We present a technique for measuring the second-order coherence function $g^{(2)}(τ)$ of light using a Hanbury-Brown Twiss intensity interferometer modified for homodyne detection. The experiment was performed entirely in the continuous variable regime at the sideband frequency of a bright carrier field. We used the setup to characterize $g^{(2)}(τ)$ for thermal and coherent states, and investigated its immunity to optical loss. We measured $g^{(2)}(τ)$ of a displaced squeezed state, and found a best anti-bunching statistic of $g^{(2)}(0) = 0.11 \pm 0.18$.
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coher…
The ability to generate and verify multipartite entanglement is an important benchmark for near-term quantum devices devices. We develop a scalable entanglement metric based on multiple quantum coherences, and demonstrate experimentally on a 20-qubit superconducting device - the IBM Q System One. We report a state fidelity of 0.5165$\pm$0.0036 for an 18-qubit GHZ state, indicating multipartite entanglement across all 18 qubits. Our entanglement metric is robust to noise and only requires measuring the population in the ground state; it can be readily applied to other quantum devices to verify …
We revisit Mandel's notion that the degree of coherence equals the degree of indistinguishability by performing Hong-Ou-Mandel- (HOM-)type interferometry with single photons elastically scattered by a cw resonantly driven excitonic transition of an InAs/GaAs epitaxial quantum dot. We present a comprehensive study of the temporal profile of the photon coalescence phenomenon which shows that photon indistinguishability can be tuned by the excitation laser source, in the same way as their coherence time. A new figure of merit, the coalescence time window, is introduced to quantify the delay below…
Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation. Finding reliable and effective methods for assessing its presence is then highly desirable. Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis. Here we experimentally measure a novel type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way. Our experiment uses a single interferometric set-up to simultaneously measure the…
We use single photon detectors to probe the motional state of a superfluid $^4$He resonator of mass $\sim1$ ng. The arrival times of Stokes and anti-Stokes photons (scattered by the resonator's acoustic mode) are used to measure the resonator's phonon coherences up to the fourth order. By post-selecting on photon detection events, we also measure coherences in the resonator when $\leq3$ phonons have been added or subtracted. These measurements are found to be consistent with predictions that assume the acoustic mode to be in thermal equilibrium with a bath through a Markovian coupling.
Entanglement between a quantum system and its environment leads to loss of coherence in the former. In general, the temporal fate of coherences is complicated. Here, we establish the connection between decoherence of a central system and fidelity decay in the environment for a variety of situations, including both, energy conserving and dissipative couplings. We show how properties of unitary time evolution of the environment can be inferred from the non-unitary evolution of coherences in the central system. This opens up promising ways for measuring Loschmidt echoes in a variety of situations…
We present methods for evaluating the rate of change in quantities during quantum evolution due to coupling to the environment (dissipation hereafter). The protocol is based on repeating a given quantum circuit (or quantum operation) twice, thrice, and so on, and measuring an expectation value after each number of repetitions. We start by applying this method for measuring the rate of purity changes in quantum circuits. This provides direct information on the quality of the circuit. Furthermore, the presented scheme enables to distill the dissipative contribution in the changes of quantities s…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively unknown. Here, we prove that encoding a system in a stabilizer code and measuring error syndromes decoheres errors, that is, causes coherent errors to converge toward probabilistic Pauli errors, even when no recovery operations are applied. Two practical consequences are that the error rate in a logical circuit is well quantified by the average gate fidelit…
We experimentally investigate the coherence properties of a qubit stored in the Zeeman substates of the 5S1/2, F=1 hyperfine ground level of a single optically trapped Rb-87 atom. Larmor precession of a single atomic spin-1 system is observed by preparing the atom in a defined initial spin-state and then measuring the resulting state after a programmable period of free evolution. Additionally, by performing quantum state tomography, maximum knowledge about the spin coherence is gathered. By using an active magnetic field stabilization and without application of a magnetic guiding field we achi…
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…
We demonstrate a new method to directly manipulate the state of individual two-level systems (TLS) in phase qubits. It allows one to characterize the coherence properties of TLS using standard microwave pulse sequences, while the qubit is used only for state readout. We apply this method to measure the temperature dependence of TLS coherence for the first time. The energy relaxation time $T_1$ is found to decrease quadratically with temperature for the two TLS studied in this work, while their dephasing time measured in Ramsey and spin-echo experiments is found to be $T_1$ limited at all tempe…
Macroscopic quantum coherence and entanglement in mechanical systems
Institute of Quantum Science；Technology \& Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, Beijing 100871, China；Department of Physics, ETH Z\" u rich, Z\" u rich 8093, Switzerland
Out-of-time-order correlations (OTOCs) characterize the scrambling, or delocalization, of quantum information over all the degrees of freedom of a system and thus have been proposed as a proxy for chaos in quantum systems. Recent experimental progress in measuring OTOCs calls for a more thorough understanding of how these quantities characterize complex quantum systems, most importantly in terms of the buildup of entanglement. Although a connection between OTOCs and entanglement entropy has been derived, the latter only quantifies entanglement in pure systems and is hard to access experimental…
The pure quantum correlations totally independent of the classical coherence of light have been experimentally demonstrated. By measuring the visibility of the interference fringes and the correlation variances of amplitude and phase quadratures between a pair of bright twin optical beams with different frequencies produced from a non-degenerate optical parametric oscillator, we found that when classical interference became worse even vanished, the quadrature quantum correlations were not influenced, completely. The presented experiment obviously shows the quantum correlations of light do not …
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…
In both classical and quantum world, information cannot appear or disappear. This fundamental principle, however, is questioned for a black hole, by the acclaimed "information loss paradox". Based on the conservation laws of energy, charge, and angular momentum, we recently show the total information encoded in the correlations among Hawking radiations equals exactly to the same amount previously considered lost, assuming the non-thermal spectrum of Parikh and Wilczek. Thus the information loss paradox can be falsified through experiments by detecting correlations, for instance, through measur…
I demonstrate a simple example of how the time series obtained from searches for ultralight bosonic dark matter (DM), such as the axion, can be used to determine whether it is in a coherent or incoherent quantum state. The example is essentially trivial, but I hope that explicitly addressing it provokes experimental exploration. In the standard coherent state, $\mathcal{O}(1)$ oscillations in the number density occur over the coherence time, $τ_c=h/m v^2$, where $m$ is the particle mass and $v$ is the galactic virial velocity, leading to a reduction in the constraining power of experiments ope…
We suggest a procedure for demonstrating quantum coherence and measuring decoherence times between different fluxoid states of a SQUID by using ``adiabatic inversion'', where one macroscopic fluxoid state is smoothly transferred into the other, like a spin reversing direction by following a slowly moving magnetic field. This is accomplished by sweeping an external applied flux, and depends on a well-defined quantum phase between the two macroscopic states. Varying the speed of the sweep relative to the decoherence time permits one to move from the quantum regime, where such a well-defined phas…
Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement basis. Unlike projection measurements, there are additional and possibly hidden degrees of freedom in apparatus for generic measurements. We propose an adversary scenario for general measurements with arbitrary input states, based on which, we characterize the intrinsic randomness. Interestingly, we discover that under certain measurements, such as the symmetr…
It is usually considered that the spectrum of an optical cavity coupled to an atomic medium does not exhibit a normal-mode splitting unless the system satisfies the strong coupling condition, meaning the Rabi frequency of the coherent coupling exceeds the decay rates of atom and cavity excitations. Here we show that this need not be the case, but depends on the way in which the coupled system is probed. Measurements of the reflection of a probe laser from the input mirror of an overdamped cavity reveal an avoided crossing in the spectrum which is not observed when driving the atoms directly an…
In this paper, we consider the quantum correlations, coherence and entanglement, in neutrino oscillation. We find that the $l_{1}$-norm as a coherence measure is equal to sum of the three possible concurrences for measuring the entanglement among different flavor modes which were calculated in the paper by (M. Blasone et al., Europhys. Lett., {\bf 112}, 20007). Our result shows that the origin of the flavor entanglement in neutrino oscillation is the same as that of quantum coherence. Furthermore, in the wave packet framework, the variation of $l_{1}$-norm is investigated by varying the wave p…
Quantum simulations with ultra-cold atoms in optical lattices open up an exciting path towards understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution, unparalleled in other quantum many-body systems. However, currently a direct measurement of local coherent currents is out of reach. In this work, we show how to achieve that by measuring densities that are altered in response to quenches to non-interacting dynamics, e.g., after tilting the optical lattice. For this, we establish a data analysis method solving th…
