Einstein Podolsky Rosen quantum correlations are discussed from the perspective of a ghost field introduced by Einstein. The concepts of ghost field, hidden variables, local reality and the Bell inequality are reviewed. In the framework of the correlated singlet state, it is shown that quantum mechanics can be cast in a way that has the form of either nonpositive and local ghost field or a positive and nonlocal ghost field.
A three-slit ghost interference experiment with entangled photons is theoretically analyzed using wave-packet dynamics. A non-local duality relation is derived which connects the path distinguishability of one photon to the interference visibility of the other.
One of the most surprising consequences of quantum mechanics is the nonlocal multi-particle interference observable in joint-detection of distant particle-detectors. Ghost imaging is one of such phenomena. Two types of ghost imaging have been experimentally demonstrated since 1995. Type-one ghost imaging uses entangled photon pairs as the light source. The nonlocal point-to-point image-forming correlation is the result of a constructive-destructive superposition among a large number of biphoton amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternative ways …
We propose and analyze a modified ghost-interference experiment, and show that revealing the particle-nature of a particle passing through a double-slit hides the wave-nature of a spatially separated particle which it is entangled with. We derive a nonlocal duality relation, ${\mathcal D}_1^2 + {\mathcal V}_2^2 \le 1$, which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohr's principle of complementarity to a nonlocal scenario. We also propose a ghost quantum eraser in which, erasing the which-path information of one particle brin…
The concept of quantum entanglement and hyper-entanglement, lying at the heart of quantum information science and technologies, is physically counter-intuitive and mathematically elusive. We design a polarization-encoded ghost imaging system based on the frame of Hardy nonlocality paradox to visualize the evidence of quantum hyper-entanglement by capturing purely nonlocal photonic events. In two-photon polarization-spatial-mode hyper-entangled state, spatial entanglement con-veys the ghost images while polarization entanglement encodes the imaging channels. Then whether imaging the single ghos…
Much more image details can be resolved by improving the system's imaging resolution and enhancing the resolution beyond the system's Rayleigh diffraction limit is generally called super-resolution. By combining the sparse prior property of images with the ghost imaging method, we demonstrated experimentally that super-resolution imaging can be nonlocally achieved in the far field even without looking at the object. Physical explanation of super-resolution ghost imaging via compressive sampling and its potential applications are also discussed.
Ghost imaging is a method to nonlocally image an object by transmitting pairs of entangled photons through the object and a reference optical system respectively. We present a theoretical analysis of the quantum noise in this imaging technique. The dependence of the noise on the properties of the apertures in the imaging system are discussed and demonstrated with a numerical example. For a given source, the resolution and the signal-to-noise ratio cannot be improved at the same time .
Certification of nonlocality of quantum mechanics is an important fundamental test that typically requires prolonged data collection and is only revealed in an in-depth analysis. These features are often particularly exposed in hybrid systems, such as interfaces between light and atomic ensembles. Certification of entanglement from images acquired with single-photon camera can mitigate this issue by exploiting multiplexed photon generation. Here we demonstrate this feature in a quantum memory (QM) operating in a real-time feedback mode. Through spatially-multimode spin-wave storage the QM enab…
In this paper, we propose a theoretical scheme of ghost imaging in terms of $N$th-order correlated thermal light. We obtain the Gaussian thin lens equations in the ghost imaging protocol. We show that it is possible to produce $N-1$ ghost images of an object at different places in a nonlocal fashion by means of a higher-order correlated imaging process with an $N$th-order correlated thermal source and correlation measurement. We investigate the visibility of the ghost images in the scheme, and obtain the upper bounds of the visibility for the $N$th-order correlated thermal-light ghost imaging.…
We propose a experimental scenario of edge enhancement ghost imaging of phase objects with nonlocal orbital angular momentum (OAM) phase filters. Spatially incoherent thermal light is separated into two daughter beams, the test and reference beams, in which the detected objects and phase filters are symmetrically placed,respectively. The results of simulation experiment prove that the edge enhanced ghost images of phase objects can be achieved through the second-order light field intensity correlation measurement owing to the OAM correlation characteristics. Further simulation results demonstr…
We address parametric-downconversion seeded by multimode pseudo-thermal fields. We show that this process may be used to generate multimode pairwise correlated states with entanglement properties that can be tuned by controlling the seed intensities. Multimode pseudo-thermal fields seeded parametric-downconversion represents a novel source of correlated states, which allows one to explore the classical-quantum transition in pairwise correlations and to realize ghost imaging and ghost diffraction in regimes not yet explored by experiments.
The currently used ghost image schemes traditionally involve two-mode entangled light states or incoherent radiation. Here, application of four-mode entangled light states is considered. It is shown that multiplexed ghost images (MGI) formed by four-mode entangled quantum light states have mutual spatial correlations determined by the 8th order field correlation functions. A special algorithm to calculate high-order correlations of Bose operators was developed. We also demonstrate that the accounting of MGI correlations allows us to improve the quality of the restored image of an object when p…
There has been an intense debate on the quantum versus classical origin of ghost imaging with a thermal light source over the last two decades. A lot of distinguished work has contributed to this topic, both theoretically and experimentally, however, to this day this quantum-classical dilemma still persists. Here we formulate for the first time a density matrix in the photon orbital angular momentum (OAM) Hilbert space to fully characterize the two-arm ghost imaging system with the basic definition of thermal light sources. Our formulation offers a mathematically precise method to describe the…
One of the possible types of n-th order ghost imaging is experimentally performed using multi-photon (higher-order) intensity correlations of pseudothermal light. It is shown that although increasing the order of intensity correlations leads to the growth of ghost imaging visibility, it at the same time reduces the signal-to-noise ratio. Therefore, ghost imaging with thermal light is optimal in the second order in the intensity.
Using path integrals we express the quantum nonlocality of AB-effect type in the form of singularity. The gauge-fixing term in path integrals induce the AB effect in ordinary scattering processes. This means that all scattering processes are accompanied by nonlocal effect. The formulae are then extended to theory of fields that additionally include a scalar potential. It turns out that the degree of freedom of nonlocality in quantum fields is just the degree of the ghosts. Furthermore, renormalization method can be related to this type of nonlocal effect.
We provide a unified treatment of classical and quantum Gaussian-state sources that unambiguously identifies which features of ghost imaging are strictly quantum mechanical. We show that ghost-image formation is fundamentally classical, with the image being expressible in terms of the phase-insensitive and phase-sensitive cross correlations between the detected fields. We then consider ghost-imaging scenarios with either phase-insensitive or phase-sensitive sources, where the former are always classical but the latter may be classical or quantum mechanical. We show that if their auto-correlati…
Quantum correlations become formidable tools for beating classical capacities of measurement. Preserving these advantages in practical systems, where experimental imperfections are unavoidable, is a challenge of the utmost importance. Here we propose and realize a quantum ghost imaging protocol able to compensate for the detrimental effect of detection noise and losses. This represents an important improvement as quantum correlations allow low brightness imaging, desirable for reducing the absorption dose. In particular, we develop a comprehensive model starting from a ghost imaging scheme ela…
Since the first quantum ghost imaging (QGI) experiment in 1995, many QGI schemes have been put forward. However, the position-position or momentum-momentum correlation required in these QGI schemes cannot be distributed over optical fibers, which limits their large geographical applications. In this paper, we propose and demonstrate a scheme for long distance QGI utilizing frequency correlated photon pairs. In this scheme, the frequency correlation is transformed to the correlation between the illuminating position of one photon and the arrival time of the other photon, by which QGI can be rea…
Arbitrary Nth-order ($N\geq2$) lensless ghost imaging with thermal light has been performed for the first time by only recording the intensities in two optical paths. It is shown that the image visibility can be dramatically enhanced as the order N increases. It is also found that longer integration times are required for higher-order correlation measurements as N increases, due to the increased fluctuations of higher-order intensity correlation functions.
It is shown that the Einstein, Podolsky and Rosen (EPR) correlations for arbitrary spin-s and the Greenberger, Horne and Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell's inequalities void. A description that exhibits the relation between the randomness and the nonlocality of entangled correlations is introduced. Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy. The nonlocal character of the EPR correlations is tested using the informati…
The theory of ghost imaging is developed in a Gaussian-state framework that both encompasses prior work - on thermal-state and biphoton-state imagers - and provides a complete understanding of the boundary between classical and quantum behavior in such systems. The core of this analysis is the expression derived for the photocurrent-correlation image obtained using a general Gaussian-state source. This image is expressed in terms of the phase-insensitive and phase-sensitive cross-correlations between the two detected fields, plus a background. Because any pair of cross-correlations is obtainab…
In this paper, we study the Hardy nonlocal argument (HNA) and the Cabello nonlocal argument (CNA) under the Information Causality, Macroscopic Locality and Local Orthogonality principles in the context of Local Randomness. We see that, in the context of all the possibilities of local randomness, the gap between the quantum mechanics and the above principles, in the Cabello's nonlocality argument is larger than the Hardy's case. Therefore the CNA is stronger control than the HNA for detecting post-quantum nosignalling correlations.
The formalism employing local complex amplitudes that resolved the Einstein-Podolsky-Rosen puzzle (C. S. Unnikrishnan, quant-ph/0001112) is applied to the three-particle GHZ correlations. We show that the GHZ quantum correlations can be reproduced without nonlocality.
It is argued that the quantum correlations are not maximally nonlocal to make it possible to control local outcomes from outside spacetime, and quantum mechanics emerges from timeless nonlocality and biased local randomness. This rules out a world described by NL (nonlocal) boxes. A new type of experiments is suggested.
Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.
It is argued that recent experiments with moving beam-splitters demonstrate that there is no real time ordering behind the nonlocal correlations: In Bell's world there is no "before" and "after".
The simulation of quantum correlations with alternative nonlocal resources, such as classical communication, gives a natural way to quantify their nonlocality. While multipartite nonlocal correlations appear to be useful resources, very little is known on how to simulate multipartite quantum correlations. We present the first known protocol that reproduces 3-partite GHZ correlations with bounded communication: 3 bits in total turn out to be sufficient to simulate all equatorial Von Neumann measurements on the 3-partite GHZ state.
Different nonlocal quantum correlations of entanglement, steering and Bell nonlocality are defined with the help of local hidden state (LHS) and local hidden variable (LHV) models. Considering their unique roles in quantum information processing, it is of importance to understand the individual nonlocal quantum correlation as well as their relationship. Here, we investigate the effects of amplitude damping decoherence on different nonlocal quantum correlations. In particular, we have theoretically and experimentally shown that the entanglement sudden death phenomenon is distinct from those of …
In this paper we investigate the nonlocal correlation (beyond entanglement) captured by measurement induced nonlocality and geometric quantum discord for a pair of interacting spin-1/2 particles at thermal equilibrium. It is shown that both the measures are identical in measuring the correlation. We show the possibility of nonlocal correlation between the spins without entanglement, which ceases to exist only for the maximal mixture of product bases. We also observe that while interaction between the spins is responsible for the enhancement of correlation, this non-classicality decreases with …
The multipartite setting offers much more complexity of nonlocality than the bipartite one. We analyze the structure of tripartite nonlocal correlations by proposing inequalities satisfied by each type: bilocal, broadcasting and quantum, but violated by the other two. One of the inequalities satisfied by broadcasting correlations is generalized for multipartite systems. The study of its quantum mechanical violation reveals that Greenberger-Horne-Zeilinger-like states exhibit new, powerful correlations.
In thermal light ghost imaging, the correlation orders were usually positive integers in previous studies. In this paper, we examine the fractional-order moments, whose correlation order are fractional numbers, between the bucket and reference signals in the ghost imaging system. The crucial step in theory is to determine the precise relation between the bucket signals and reference signals. We deduce the joint probability density function between the bucket and reference signals by regarding the reference signals as an array of independent stochastic variables. In calculating the fractional-o…
We present six new measures of nonlocal correlation for discrete multipartite quantum systems; correlance, statance, probablance, strong discordance, discordance, and diagonal discordance. The correlance measures all nonlocal correlation (even bound entanglement), and is exactly computable for all pure and mixed states. Statance and probablance are not yet computable, but motivate the strong discordance (for nonlocal correlation beyond that achievable by a strictly classical state), discordance (a measure of all nonlocal correlation in distinguishably quantum states), and diagonal discordance …
Quantum mechanics and relativistic causality together imply nonlocality: nonlocal correlations (that violate the CHSH inequality) and nonlocal equations of motion (the Aharonov-Bohm effect). Can we invert the logical order? We consider a conjecture that nonlocality and relativistic causality together imply quantum mechanics. We show that correlations preserving relativistic causality can violate the CHSH inequality more strongly than quantum correlations. Also, we describe nonlocal equations of motion, preserving relativistic causality, that do not arise in quantum mechanics. In these nonlocal…
Correlation boxes are hypothetical systems capable of producing the maximal algebraic violation of Bell inequalities, beyond the quantum bound and without superluminal signaling. The fact that these systems show stronger correlations than those presented by maximally entangled quantum states has been regarded as a demonstration that the former are more nonlocal than the latter. By employing an alternative, consistent measure of nonlocality, we show that this conclusion is not necessarily true. In addition, we find a class of correlation boxes that are less nonlocal than the quantum singlet wit…
Coincidence detection is a key technique used in nonlocal quantum-correlation measurements to test Bell inequality violation between remotely separated local detectors. With individual uniform intensity of local measurements, the nonlocal correlation fringe is a mysterious quantum feature that cannot be achieved classically. Here, the coincidence detection is coherently investigated to understand the fundamental physics of the nonlocal correlation fringe via second-order quantum superposition between selected nonlocal measurement events. Because of the coherence feature of paired photons, the …
We show that no probability distribution of spin measurement outcomes on pairs of spin 1/2 particles is unambiguously more nonlocal than the quantum correlations. That is, any distribution that produces a CHSH violation larger than the quantum violation for some axis choices also produces a smaller CHSH violation for some other axis choices. In this sense, it is not possible for nature to be strictly more nonlocal than quantum theory allows.
Composite quantum systems exhibit non-local correlations. These counter intuitive correlations form a resource for quantum information processing and quantum computation. In our previous work on two qubit maximally entangled mixed states, we observed that entangled states, states that can be used for quantum teleportaion, states that violate Bell-CHSH inequality and states that do not admit local hidden variable description is the hierarchy in terms of the order of nonlocal correlations. In order to establish this hierarchy, in the present work, we investigate the effect of noise on two quibt …
Through scanned coincidence counting, we probe the quantum image produced by parametric down conversion with a pump beam carrying orbital angular momentum. Nonlocal spatial correlations are manifested through splitting of the coincidence spot into two.
Many three-party correlations, including some that are commonly described as genuinely tripartite nonlocal, can be simulated by a network of underlying subsystems that display only bipartite nonsignaling nonlocal behavior. Quantum mechanics predicts three-party correlations that admit no such simulation, suggesting there are versions of nonlocality in nature transcending the phenomenon of bipartite nonsignaling nonlocality. This paper introduces a rigorous framework for analyzing tripartite correlations that can be simulated by bipartite-only networks. We confirm that expected properties of so…
We reexamine quantum correlation from the fundamental perspective of its consanguineous quantum property, the coherence. We emphasize the importance of specifying the tensor product structure of the total state space before discussing quantum correlation. A measure of quantum correlation for arbitrary dimension bipartite states using nonlocal coherence is proposed, and it can be easily generalized to the multipartite case. The quantification of non-entangled component within quantum correlation is investigated for certain states.
Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and associated to fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality that appears in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy and full random outcomes are thus highly desired properties for multipartite correlations in intrinsically genuine-multipartite cryptographic scenarios. We prove that local measurements on Greenberger-Ho…
Franson-type nonlocal correlation is a testing tool for Bell inequality violation using noninterfering interferometers, where coincidence measurements involve an interference fringe of g^((1)) correlation between noninterfering photon pairs. Like the Bell inequality, Franson correlation is also limited to a microscopic regime of entangled photon pairs. Here, randomness-based macroscopic Franson-type nonlocal correlation is presented using polarization-basis coherent superposition of laser light, where probabilistic randomness between bipartite orthonormal bases plays an important role for both…
The problem of nonlocality in the dynamical three-body Casimir-Polder interaction between an initially excited and two ground-state atoms is considered. It is shown that the nonlocal spatial correlations of the field emitted by the excited atom during the initial part of its spontaneous decay may become manifest in the three-body interaction. The observability of this new phenomenon is discussed.
In this paper we study the correlations that arise when two separated parties perform measurements on systems they hold locally. We restrict ourselves to those correlations with which arbitrarily fast transmission of information is impossible. These correlations are called nonsignaling. We allow the measurements to be chosen from sets of an arbitrary size, but promise that each measurement has only two possible outcomes. We find the structure of this convex set of nonsignaling correlations by characterizing its extreme points. Taking an information-theoretic view, we prove that all of these ex…
The monogamy relations satisfied by quantum correlation measures play important roles in quantum information processing. Generally they are given in summation form. In this note, we study monogamy relations in product form. We present product-form monogamy relations for Bell nonlocality for three-qubit and multi-qubit quantum systems. We then extend our studies to other quantum correlations such as concurrence.
Quantum mechanics permits nonlocality - both nonlocal correlations and nonlocal equations of motion - while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality: "superquantum" correlations, and nonlocal "jamming" of correlations. These models are consistent with some definitions of nonlocality and causality.
Quantum mechanics is a nonlocal theory, but not as nonlocal as the no-signalling principle allows. However, there exist quantum correlations that exhibit maximal nonlocality: they are as nonlocal as any non-signalling correlations and thus have a local content, quantified by the fraction $p_L$ of events admitting a local description, equal to zero. Exploiting the link between the Kochen-Specker and Bell's theorems, we derive, from every Kochen-Specker proof, Bell inequalities maximally violated by quantum correlations. We then show that these Bell inequalities lead to experimental bounds on th…
In honor of Daniel Greenberger's 65th birthday I record for posterity two superb examples of his wit, offer a proof of an important theorem on quantum correlations that even those of us over 60 can understand, and suggest, by trying to make it look silly, that invoking ``quantum nonlocality'' as an explanation for such correlations may be too cheap a way out of the dilemma they pose.
In this article, we investigate the dynamics of a bipartite system under the action of a local non-Hermitian system. We study the quantum correlation of the bipartite system quantified by the entanglement, measurement-induced nonlocality (MIN) based on Hilbert-Schmidt norm, trace distance, and Bell inequality. We find that the quantum correlations of the system depend on the initial conditions and system parameters. We observe that the states with nonzero quantum correlation obey the Bell inequality even in the absence of entanglement. Moreover, the Bell inequality completely fails to manifest…
Indistinguishability is an essential concept to understanding mysterious quantum features in the view point of the wave-particle duality of quantum mechanics. The fundamental physics of the indistinguishability lies in quantum superposition of a single photon via orthogonal bases in a Hilbert space. Here, a pure coherence approach is applied to the nonlocal correlation using coherent photons manipulated for polarization-frequency correlation. For this, both wave mixing and heterodyne detection techniques are applied for the delayed-choice experiments of a quantum eraser using coherent photons …
One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has started to play important roles in practical engineering applications. Quantum imaging is one of these exciting areas. Quantum imaging has demonstrated two peculiar features: (1) reproducing "ghost" images in a "nonlocal" manner, and (2) enhancing the spatial resolution of imaging beyond the diffraction limit. In this article, we start with the review of classical imaging to est…
In instantaneous nonlocal quantum computation, two parties cooperate in order to perform a quantum computation on their joint inputs, while being restricted to a single round of simultaneous communication. Previous results showed that instantaneous nonlocal quantum computation is possible, at the cost of an exponential amount of prior shared entanglement (in the size of the input). Here, we show that a linear amount of entanglement suffices, (in the size of the computation), as long as the parties share nonlocal correlations as given by the Popescu-Rohlich box. This means that communication is…
Franson-type nonlocal quantum correlation based on the particle nature of quantum mechanics has been intensively studied for both fundamental physics and potential applications of quantum key distribution between remotely separated parties over the last several decades. Recently, a coherence theory of deterministic quantum features has been applied for Franson-type nonlocal correlation [arXiv:2102.06463] to understand its quantumness in a purely classical manner, where the resulting features are deterministic and macroscopic. Here, nearly sub-Poisson distributed coherent photon pairs obtained …
A transparent polarisation sensitive phase pattern exhibits a position and polarisation dependent phase shift of transmitted light and it represents a unitary transformation. A quantum ghost image of this pattern is produced with hyper-entangled photons consisting of Einstein-Podolsky-Rosen (EPR) and polarisation entanglement. In quantum ghost imaging, a single photon interacts with the pattern and is detected by a stationary detector and a non-interacting photon is imaged on a coincidence camera. EPR entanglement manifests spatial correlations between an object plane and a ghost image plane, …
Indistinguishability in quantum mechanics is an essential concept to understanding mysterious quantum features such as self-interference of a single photon and two-photon nonlocal correlation. Delayed-choice experiments are for the cause-effect violation via post-measurements of photons in an interferometric system. Recently, a macroscopic version of the delayed-choice experiments has been demonstrated using the classical means of Poisson distributed photons in a noninterfering Mach-Zehnder interferometer (NMZI). Here, a coherence version of the nonlocal correlation is presented using the wave…
In this thesis, we study about three subjects 1- Classical simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements, 2- Quantum correlations in successive single spin measurements, 3- Non locality without inequality for almost all two-qubit entangled states based on Cabello's non locality argument.
