The concept of physical twin observables (PTO) for bipartite quantum states,introduced and proved relevant for quantum information theory in recent work, is substantially simplified. The relation of observable and state is studied in detail from the point of view of coherence entropy. Properties of this quantity are further explored. It is shown that, besides for pure states, quantum discord (measure of entanglement) can be expressed through the coherence entropy of a PTO complete in relation to the state.
Properties of weak spatio-spectral twin beams in paraxial approximation are analyzed using the decomposition into appropriate paired modes. Numbers of paired modes as well as numbers of modes in the signal (or idler) field in the transverse wave-vector and spectral domains are analyzed as functions of pump-beam parameters. Spatial and spectral coherence of weak twin beams is described by auto- and cross-correlation functions. Relation between the numbers of modes and coherence is discussed.
Strong correlations between the signal and idler beams imprinted during their generation dominantly determine the properties of twin beams. They are also responsible for the waves in intensity coherence observed in the wave-vector space of a twin beam propagating in a nonlinear crystal in the regime with pump depletion. These waves start to develop at certain twin-beam intensity and move from the signal and idler beam centers towards their tails. They manifest themselves via the change of coherence volume monitored in the far field by the measurement of local modified $ \bar{g}^{(2)} $ functio…
Nonclassicality, entanglement, as well as dimensionality of a noisy twin beam are determined using characteristic function of the beam written in the Fock basis. One-to-one correspondence between the negativity quantifying entanglement and the nonclassicality depth is revealed. Twin beams, which are either entangled or nonclassical (independent of their entanglement), are observed only for the limited degrees of noise that degrades their quantumness. Dimensionality of the twin beam quantified by the participation ratio is compared with the dimensionality of entanglement determined from the neg…
Using the model of parametric interaction based on the spatio-spectral Schmidt modes and generalized parametric approximation, we analyze coherence and mode structure of ultra-intense twin beams generated in the regime with pump depletion. We show that the increase of spatial and spectral coherence with the increasing pump power observed for moderate powers is replaced by the decrease for the pump powers at which pump depletion occurs. This behavior of coherence is opposed to that exhibited by the number of spatio-spectral modes effectively constituting the twin beam. The conditions for maxima…
Gradual loss of the entanglement of a twin beam containing around 25 photon pairs with the increasing external noise is experimentally investigated. The entanglement is quantified by the non-classicality depths and the non-classicality counting parameters related to several non-classicality criteria. The reduction of intensity moments of the analyzed multi-mode twin beams to single-mode ones allows to determine the negativity as another quantifier of the entanglement. Both the raw photocount histograms and the reconstructed photon-number distributions are analyzed in parallel.
This work analyses the temporal coherence and correlation of twin beams generated in a quasi-phase matched nonlinear crystal in a counterpropagating configuration, ranging from the low-gain regime, where counterpropagating photon pairs are generated spontaneously, to the regime of stimulated pair production, close to the MOPO (Mirrorless Optical Parametric Oscillator) threshold. Here we show a critical divergence of the correlation time and slowing down of quantum fluctuations originating from the feedback mechanism responsible of the MOPO threshold.
Spatio-spectral properties of twin beams at their transition from low to high intensities are analyzed in parametric and paraxial approximations using the decomposition into paired spatial and spectral modes. Intensity auto- and cross-correlation functions are determined and compared in the spectral and temporal domains as well as the transverse wave-vector and crystal output planes. Whereas the spectral, temporal and transverse wave-vector coherence increases with the increasing pump intensity, coherence in the crystal output plane is practically independent on the pump intensity owing to the…
Continuing the study of mixed-state entanglement in terms of opposite-subsystem observables the measurement of one of which amounts to the same as that of the other (so-called twins), begun in a recent article, so-called strong twin events, which imply biorthogonal mixing of states, are defined and studied. It is shown that for each mixed state there exists a Schmidt canonical (super state vector) expansion in terms of Hermitian operators, and that it can be the continuation of the mentioned biorthogonal mixing due to strong twins. The case of weak twins and nonhermitian Schmidt canonical expa…
In this work we analyse and compare the continuous variable tripartite entanglement available from the use of two concurrent or cascaded $χ^{(2)}$ nonlinearities. We examine both idealised travelling-wave models and more experimentally realistic intracavity models, showing that tripartite entangled outputs are readily producible. These may be a useful resource for such applications as quantum cryptography and teleportation.
We demonstrate production of quantum correlated and entangled beams by second harmonic generation in a nonlinear resonator with two output ports. The output beams at wavelength 428.5 nm exhibit 0.9 dB of nonclassical intensity correlations and 0.3 dB of entanglement.
This work describes the continuous-variable entanglement of the counter-propagating twin beams generated in a Mirrorless Optical Parametric Oscillator below threshold, encompassing both their quadrature and photon-number correlation. In the first case, a comparison with the single-pass co-propagating geometry outlines the huge difference of the bandwidth involved and a completely different stability of the two sources with respect to the phase-angle. In the second case, stimulated by the critical divergence of the correlation time evidenced by Corti et al., we address the issue of the temporal…
We show that spatial entanglement of two twin images obtained by parametric down-conversion is complete, i.e. concerns both amplitude and phase. This is realised through a homodyne detection of these images which allows for measurement of the field quadrature components. EPR correlations are shown to exist between symmetrical pixels of the two images. The best possible correlation is obtained by adjusting the phase of the local oscillator field (LO) in the area of maximal amplification. The results for quadrature components hold unchanged even in absence of any input image i.e. for pure parame…
The quantum entanglement of amplitude and phase quadratures between two intense optical beams with the total intensity of 22mW and the frequency difference of 1nm, which are produced from an optical parametric oscillator operating above threshold, is experimentally demonstrated with two sets of unbalanced Mach-Zehnder interferometers. The measured quantum correlations of intensity and phase are in reasonable agreement with the results calculated based on a semi-classical analysis of the noise characteristics given by C. Fabre et al.
In this paper, the theory of coherence frame is developed. Two kinds of coherence frame are classified. Under coherence frame, the entanglement is conserved in the entanglement swapping process, without entanglement sudden death and birth. The einselection method for the preferred basis problem in the entangle process is shown as incomplete.
In this work we derive analytical relations between Entanglement and Coherence as well as between Discord and Coherence, for Bell-diagonal states and for X states, evolving under the action of several noise channels: Bit Flip, Phase Damping and Depolarizing. We demonstrate that for these families, Coherence is the fundamental correlation, that is: Coherence is necessary for the presence of Entanglement and Discord.
Quantum states of light with multiple spatial modes are fundamental for quantum imaging and parallel quantum information processing. Thus, their characterization, which can be achieved through measurements of the coherence area, is an important area of research. We present a comparative study between two different measurement techniques for the coherence area of bright entangled twin beams of light generated with a four-wave mixing process in a hot rubidium vapor cell. The first one provides a direct characterization of the size of the coherence area and is based on correlation measurements be…
We propose a photonics-based, continuous-variable (CV) form of remote entanglement utilizing strictly second-order nonlinear optical interactions that does not require the implementation of a state-projective measurement (i.e. remote entanglement without conditioning). This scheme makes use of two separate down-converters, wherein the corresponding nonlinear crystals are driven by strong classical fields as prescribed by the parametric approximation, as well as a fully quantum mechanical model of nondegenerate second harmonic generation (SHG) whose evolution is described by the trilinear Hamil…
Large-scale quantum communication networks are still a huge challenge due to the rate-distance limit of quantum key distribution (QKD). Recently, twin-field (TF) QKD has been proposed to overcome this limit. Here, we prove that coherent-state-based TF-QKD is a time-reversed entanglement protocol, where the entanglement generation is realized with entanglement swapping operation via an entangled coherent state measurement. We propose a coherent-state-based TF-QKD with optimal secret key rate under symmetric and asymmetric channels by using coherent state and cat state coding. Furthermore, we sh…
Twin-beam coherence properties are analyzed both in the spatial and spectral domains at high-gain regime including pump depletion. The increase of the size of intensity auto- and cross-correlation areas at increasing pump power is replaced by a decrease in the pump depletion regime. This effect is interpreted as a progressive loss in the mode selection occurring at high-gain amplification. The experimental determination of the number of spatio-spectral modes from $g^{(2)} $-function measurements confirms this explanation.
This work analyses the temporal coherence and correlation of counterpropagating twin photons generated in a quasi-phase matched nonlinear cristal by spontaneous parametric-down conversion. We find out different pictures depending on the pump pulse duration relative to two characteristic temporal scales, determined respectively by the temporal separation between the counter-propagating and the co-propagating wavepackets. When the pump duration is intermediate between the two scales, we show a transition from a highly entangled state to an almost separable state, with strongly asymmetric spectra…
With atomic spontaneously generated coherence (SGC), we propose a novel scheme to coherently control the atom--photon momentum entanglement through atomic internal coherence. A novel phenomena of ``phase entanglement in momentum'' is proposed, and we found, under certain conditions, that super--high degree of momentum entanglement can be produced with this scheme.
We draw an intuitive picture of the spatio-temporal properties of the entangled state of twin photons, where they are described as classical wave-packets. This picture predicts a precise relation between their temporal and transverse spatial separations at the crystal output. The space-time coupling described by classical arguments turns out to determine in a precise way the spatio-temporal structure of the quantum entanglement, analysed by means of the biphotonic correlation and of the Schmidt dimensionality of the entanglement.
We establish a general operational one-to-one mapping between coherence measures and entanglement measures: Any entanglement measure of bipartite pure states is the minimum of a suitable coherence measure over product bases. Any coherence measure of pure states, with extension to mixed states by convex roof, is the maximum entanglement generated by incoherent operations acting on the system and an incoherent ancilla. Remarkably, the generalized CNOT gate is the universal optimal incoherent operation. In this way, all convex-roof coherence measures, including the coherence of formation, are end…
Coherence and entanglement are fundamental concepts in resource theory. The coherence (entanglement) of assistance is the coherence (entanglement) that can be extracted assisted by another party with local measurement and classical communication. We introduce and study the general coherence of assistance. First, in terms of real symmetric concave functions on the probability simplex, the coherence of assistance and the entanglement of assistance are shown to be in one-to-one correspondence. We then introduce two classes of quantum states: the assisted maximally coherent states and the assisted…
Spatial entanglement is at the heart of quantum enhanced imaging applications and high-dimensional quantum information protocols. In particular, for imaging and sensing applications, quantum states with a macroscopic number of photons are needed to provide a real advantage over the classical state-of-the-art. We demonstrate the Einstein-Podolsky-Rosen (EPR) paradox in its original position and momentum form with bright twin beams of light by showing the presence of EPR spatial (position-momentum) entanglement. An electron-multiplying charge-coupled-device camera is used to record images of the…
We study the evolution of twin-beam propagating inside active media that may be used to establish a continuous variable entangled channel between two distant users. In particular, we analyze how entanglement is degraded during propagation, and determine a threshold value for the interaction time, above which the state become separable, and thus useless for entanglement based manipulations. We explicitly calculate the fidelity for coherent state teleportation and show that it is larger than one half for the whole range of parameters preserving entanglemenent.
Originated from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels with the help of quantum entanglement. By explicitly computing the minimal error probability of channel discrimination, it is shown that entanglement can enhance the capacity of coherence-breaking channel distinguishability with same types for some cases while cannot enhanced for some other cases. For coherence-breaking channels with different types, the chann…
We give a simple example of the tight connection between entanglement and coherence for pure bipartite systems showing the double role played by entanglement; it allows for the creation of superpositions of macroscopic objects but at the same time makes subsystems lose their quantum mechanical coherence. For this we study the time evolution of the spin coherence in the Stern-Gerlach (SG) experiment. We also show that, contrary to the naive intuition, the spin coherence is lost before the two beams become separated in the spatial coordinates.
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is essentially the normalized coherence of the entangled state in its Schmidt basis. Its value is 1 for maximally entangled states, and 0 for separable states, irrespective of the dimensionality of the Hilbert space. So a maximally entangled state is also the one which is maximally coherent in its Schmidt basis. Quantum entanglement and quantum coherence are thus intima…
Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this, we conceive a relative entropy type quantity to account for the quantum resources of quantum measurements. The quantum coherence of a quantum measurement can be converted into the entanglement in a bipartite quantum measurement through coherence-non generating transformations. Conversely, a quantum entanglement monotone of quantum measurements induces a quan…
We show that the symmetric portion of correlated coherence is always a valid quantifier of entanglement, and that this property is independent of the particular choice of coherence measure. This leads to an infinitely large class of coherence based entanglement monotones, which is always computable for pure states if the coherence measure is also computable. It is already known that every entanglement measure can be constructed as a coherence measure. The results presented here show that the converse is also true. The constructions that are presented can also be extended to also include more g…
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…
We present a scheme well-suited to investigate quantitatively the angular momentum coherence of molecular fragments. Assuming that the dissociated molecule has a null total angular momentum, we investigate the propagation of the corresponding atomic fragments in the apparatus. We show that the envisioned interferometer enables one to distinguish unambiguously a spin-coherent from a spin-incoherent dissociation, as well as to estimate the purity of the angular momentum density matrix associated with the fragments. This setup, which may be seen as an atomic analogue of a twin-photon interferomet…
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.
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…
We establish a set of resource conversion relationships between quantum coherence and multipartite entanglement in many-body systems, where the operational measures of resource cost and distillation are focused. Under the multipartite incoherent operation, the initial coherence of single-party system bounds the maximal amounts of corresponding operational entanglement in an arbitrary bipartite partition as well as the genuine multipartite entanglement in many-body systems. Furthermore, the converted multipartite entanglement can be transferred to its subsystems and restored to coherence of a s…
The entanglement of two dipole-coupled atoms with nondegenerate two-photon transitions interacting with two-mode field in lossless cavity has been investigated. It shows that the entanglement is dependent on the initial atomic states. The possibility of considerable growth of atomic entanglement due atomic coherence and dipole-dipole interaction is shown in the case of great mean values of thermal photons.
Greenberger-Horne-Zeilinger (GHZ) states and their mixtures exhibit fascinating properties. A complete basis of GHZ-states can be constructed by properly choosing local basis rotations. We demonstrate this experimentally for the Hilbert space C2x4 by entangling two photons in polarisation and orbital angular momentum. Mixing GHZ-states unmasks different entanglement features based on their particular local geometrical connectedness. In particular, a specific GHZ-state in a complete orthonormal basis has a twin GHZ-state for which equally mixing leads to full separability in opposition to any o…
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction of the system state. We show that one can extract quantitative bounds to the relative entropy of coherence and the coherent information, coherence and entanglement quantifiers respectively, by a limited number of purity measurements. The scheme is readily implementable with current technology to verify quantum computations in large scale registers, without c…
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…
We experimentally realize the internal and external entanglement tradeoff, which is a new kind of entanglement monogamy relation different from that usually discussed. Using a source of twin photons, we find that the external entanglement in polarization of twin photons, and the path-polarization internal entanglement of one photon, limit each other. In the extreme case, when the internal state is maximally entangled, the external entanglement must be vanishing, that illustrate entanglement monogamy. Our results of the experiment coincide with the theoretical predictions, and therefore provide…
We investigate the connection between quantum resources and extractable work in quantum batteries. We demonstrate that quantum coherence in the battery or the battery-charger entanglement is a necessary resource for generating nonzero extractable work during the charging process. At the end of the charging process, we also establish a tight link of coherence and entanglement with the final extractable work: coherence naturally promotes the coherent work while coherence and entanglement inhibit the incoherent work. We also show that obtaining maximally coherent work is faster than obtaining max…
A pulsed source of energy-time entangled photon pairs pumped by a standard laser diode is proposed and demonstrated. The basic states can be distinguished by their time of arrival. This greatly simplifies the realization of 2-photon quantum cryptography, Bell state analyzers, quantum teleportation, dense coding, entanglement swapping, GHZ-states sources, etc. Moreover the entanglement is well protected during photon propagation in telecom optical fibers, opening the door to few-photon applications of quantum communication over long distances.
Quantum resource theories provide a diverse and powerful framework for extensively studying the phenomena in quantum physics. Quantum coherence, a quantum resource, is the basic ingredient in many quantum information tasks. It is a subject of broad and current interest in quantum information, and many new concepts have been introduced and generalized since its establishment. Here we show that the block coherence can be transformed into entanglement via a block incoherent operation. Moreover, we find that the POVM-based coherence associated with block coherence through the Naimark extension act…
Quantum entanglement and coherence are two fundamental features of nature, arising from the superposition principle of quantum mechanics. While considered as puzzling phenomena in the early days of quantum theory, it is only very recently that entanglement and coherence have been recognized as resources for the emerging quantum technologies, including quantum metrology, quantum communication, and quantum computing. In this work we study the limitations for the interconversion between coherence and entanglement. We prove a fundamental no-go theorem, stating that a general resource theory of sup…
Bell inequality is a mathematical inequality derived using the assumptions of locality and realism. Its violation guarantees the existence of quantum correlations in a quantum state. Bell inequality acts as an entanglement witness in the sense that a pure bipartite quantum state, having nonvanishing entanglement, always violates a Bell inequality. We construct Bell-type inequalities for product states in quantum coherence theory for different measures of coherence, and find that the maximally entangled states violate these inequalities. We further show that Bell-type inequalities for relative …
Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to quantify entanglement and coherence based on the full information of the experimentally realized multipartite states. Fortunately, other methods have been found to directly measure the fidelity of experimental states without quantum state tomography. Here we present a fidelity-based method to derive experimentally accessible lower bounds for measures of genuin…
With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole dipole interactions. As opposed to the calculation of the MQ coherence intensity based on the density matrix describing the spin system as a whole, we consider the "differentiated" intensity related only to the chosen spin pair based on the reduced density matrix. It is shown that the entanglement and the MQ coherence have similar dynamics only for nearest nei…
The remote control of coherence is a crucial step for its application in quantum computation. We investigate the maximal steered coherence (MSC) and its conversion to entanglement in multiple bosonic reservoirs. It is shown that the MSC decays with time in the Markovian regime and behaves as damped oscillations in the non-Markovian regime. The MSC can also be connected directly to the strength of non-Markovianity, through which we show that it can be noticeably enhanced by taking full advantage of the non-Markovian effects. Besides, the MSC can be converted completely to entanglement via optim…
Quantum coherence as an important quantum resource plays a key role in quantum theory. In this paper, using entropy-based measures, we investigate the relations between quantum correlated coherence, which is the coherence between subsystems [K. C. Tan, H. Kwon, C. Y. Park, and H. Jeong, Phys. Rev. A 94, 022329 (2016)], and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement meas…
Quantum devices are systems that can explore quantum phenomena, like entanglement or coherence, for example, to provide some enhancement performance concerning their classical counterparts. In particular, quantum batteries are devices that use entanglement as main element in its high performance in the charging powerful. In this paper, we explore the quantum battery performance and its relationship with the amount of entanglement that arises during the charging process. By using a general approach to a two and three-cell battery, our results suggest that entanglement is not the main resource t…
We suggest a formalism to illustrate the entanglement of identical particles in the first quantization language (1QL). Our 1QL formalism enables one to exploit all the well-established quantum information tools to understand the indistinguishable ones, including the reduced density matrix and familiar entanglement measures. The rigorous quantitative relation between the amount of entanglement and the spatial coherence of particles is possible in this formalism. Our entanglement detection process is a generalization of the entanglement extraction protocol for identical particles with mode split…
