For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is strictly greater than the average entanglement of its eigenstates. On the other hand, we show that for any complete measurement in d x d dimensions that is invariant under all local Pauli operations, the cost of the measurement is exactly equal to the average entanglement of the states associated with the outcomes.
Nonlocal gate operation is based on sharing an ancillary pair of qubits in perfect entanglement. When the ancillary pair are partially entangled, the efficiency of the gate operation drops. Using general transformations, we devise probabilistic nonlocal gates, which perform the nonlocal operation conclusively when the ancillary pair are only partially entangled. We show that a controlled purification protocol can be implemented by the probabilistic nonlocal operation.
We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local hidden-variable model in the Bell scenario. We present a fully-biseparable three-qubit bound entangled state with a local model for the most general (non-sequential) measurements. This proves for the first time that bound entangled states can admit a local model for general measurements. We furthermore show that the local model breaks down when suitable local filters ar…
Entanglement and Bell nonlocality are used to describe quantum inseparabilities. Bell-nonlocal states form a strict subset of entangled states. A natural question arises concerning how much territory Bell nonlocality occupies entanglement for a general two-qubit entangled state. In this work, we investigate the relation between entanglement and Bell nonlocality by using lots of randomly generated two-qubit states, and give out a constraint inequality relation between the two quantum resources. For studying the upper or lower boundary of the inequality relation, we discover maximally (minimally…
Localizability of entanglement in fully inseparable states is a key ingredient of assisted quantum information protocols as well as measurement-based models of quantum computing. We investigate the existence of fully inseparable states with nonlocalizable entanglement, that is, with entanglement which cannot be localized between any pair of subsystems by any measurement on the remaining part of the system. It is shown, that the nonlocalizable entanglement occurs already in suitable mixtures of a three-qubit GHZ state and white noise. Further, we generalize this set of states to a two-parametri…
Nonlocality and entanglement are not only the fundamental characteristics of quantum mechanics but also important resources for quantum information and computation applications. Exploiting the quantitative relationship between the two different resources is of both theoretical and practical significance. The common choice for quantifying the nonlocality of a two-qubit state is the maximal violation of the Clauser-Horne-Shimony-Holt inequality. That for entanglement is entanglement of formation, which is a function of the concurrence. In this paper, we systematically investigate the quantitativ…
Energy-time entangled biphoton source plays a great role in quantum communication, quantum metrology and quantum cryptography due to its strong temporal correlation and capability of nonlocal dispersion cancellation. As a quantum effect, nonlocal dispersion cancellation is further proposed as an alternative way for nonlocality test of continuous variable entanglement via the violation of Bell-like inequality proposed by Wasak et al. [Phys. Rev. A, 82, 052120 (2010)]. However, to date there is no experimental report either on the inequality violation or on a nonlocal detection with single-photo…
The construction of nonlocal sets of quantum states has attracted much attention in recent years. We first introduce two Lemmas related to the triviality of orthogonality-preserving local measurements. Then we propose a general construction of nonlocal set of $n(d-1)+1$ orthogonal product states in $(\mathbb{C}^{d})^{\otimes n}$. The sets of nonlocal orthogonal product states are also put forward for the multipartite quantum systems with arbitrary dimensions. Our novel construction gives rise to nonlocal sets of orthogonal product states with much less members and thus reveals the phenomenon o…
"action at a distance" is a weird concept in quantum theory which people always avoid mentioning in most occasions. In this work, without involving any concept about "action at a distance", we naturally construct a physical structure that resembles quantum entanglement only based on the nonlocality of the wave function. To achieve this, we propose a nonlocal structure of the single particle wave function by means of a double-well potential model. In order to better describe this nonlocal system, we have also developed two kinds of representations: local representation and nonlocal representati…
Measuring a nonlocal observable on a space-like separated quantum system is a resource-hungry and experimentally challenging task. Several theoretical measurement schemes have already been proposed to increase its feasibility, using a shared maximally-entangled ancilla. We present a new approach to this problem, using the language of generalized quantum measurements, to show that it is actually possible to measure a nonlocal spin product observable without necessarily requiring a maximally-entangled ancilla. This approach opens the door to more economical arbitrary-strength nonlocal measuremen…
We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed "quantum nonlocality without entanglement." We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72(2), compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.
We investigate how nonlocal entanglement, as identified by violations of a Bell inequality, may be protected during the evolution. Our system consists of two qubits each embedded in a bosonic reservoir evolving independently and initially in an entangled mixed state. We show that the violation of the Bell inequality can be related to the single-qubit population of excited state in such a way that, by appropriately choosing structured environments that give rise to sufficiently high values of population trapping, long-time protection of nonlocal entanglement can be correspondingly achieved.
We consider a special kind of mixed states -- a {\it Werner derivative}, which is the state transformed by nonlocal unitary -- local or nonlocal -- operations from a Werner state. We show the followings. (i) The amount of entanglement of Werner derivatives cannot exceed that of the original Werner state. (ii) Although it is generally possible to increase the entanglement of a single copy of a Werner derivative by LQCC, the maximal possible entanglement cannot exceed the entanglement of the original Werner state. The extractable entanglement of Werner derivatives is limited by the entanglement …
We propose a new scheme for realizing nonlocal nondegenerate optical parametric amplifier by means of genuine four-mode entanglement. The nondegenerate optical parametric amplifier is regarded as a unitary transformation from two input fields to two outputs. Two inputs and two outputs are located at the remote stations respectively. Employing off-line four-mode entanglement, homodyne detection, classical communication and local displacement, the nonlocal nondegenerate optical parametric amplifier can be achieved. This scheme can be implemented with a setup that is experimentally accessible at …
We present an efficient way for measuring the entanglement of the atoms. Through the auxiliary single photons input-output process in cavity quantum electrodynamics (QED), the concurrence of the atomic entanglement can be obtained according to the success probability of picking up the singlet states of the atoms. This protocol has three advantages: First, we do not require the sophisticated controlled-not (CNOT) gates. Second, the distributed atoms are not required to intact with each other. Third, the atomic entanglement can be distributed nonlocally, which provides its important applications…
Recently, it has been realized that nonlocal disentanglement may take a finite time as opposite to the asymptotic decay of local coherences. We find in this paper that a sudden irreversible death of entanglement takes place in a two atom optical Stern-Gerlach model. In particular, the one degree non dissipative environment here considered suddenly destroys the initial entanglement of any Bell's states $\ket{ϕ^{\pm}}$ superposition.
The paper titled "Tripartite entanglement versus tripartite nonlocality in 3-qubit GHZ-class states", (Physical Review Letters 102, 250404 (2009)), does very important work on studying the nature of Svetlichny Inequalities (which are Bell-type inequalities) and sheds light on some important properties and relationship between Svetlichny inequality and tripartite entanglement. It derives a result for the maximum expectation value of Svetlichny operator for GGHZ and MS states. In this comment, it is put forth that there is probably a mistake in the central result derived in the paper.
While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove t…
We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for $N$-qubit pure states (PRA \textbf{77}, 062334 (2008)). Our procedure reproduces the earlier results (PRL \textbf{87}, 137901 (2001)). The geometric method has the distinct advantage that it gives an experimental way to monitor the process of optimizing entanglement production.
Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely projective measurements. Here we prove that entanglement, one-way steering, two-way steering and nonlocality are genuinely different considering general measurements, i.e. single round positive-operator-valued-measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reve…
The utilization and control of nonlocal quantum interactions is an area of active investigation. This is not limited to subatomic structures but extends to the macroscopic level. Nonlocal interactions can be from either entanglement or path indistinguishability (the path integral for larger systems), with the latter being further subdivided as discussed. These two distinct phenomenon have recently been treated often in the literature as essentially identical, which is problematic when utilizing them for practical applications. The confusion may lie in misunderstanding the physics of the type I…
In 1927, at the Solvay conference, Einstein posed a thought experiment with the primary intention of showing the incompleteness of quantum mechanics; to prove it, he uses the instantaneous nonlocal effects caused by the collapse of the wave function of a single particle -the spooky action at a distance-, when a measurement is done. This historical event precede the well-know Einstein-Podolsk-Rosen criticism over the incompleteness of quantum mechanics. Here, by using the Stern-Gerlach experiment (SGE), we demonstrate how the instantaneous nonlocal feature of the collapse of the wave function t…
Bound entanglement, being entangled yet not distillable, is essential to our understandings of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we shall construct such kind of nonlocal bound entangled states for all finite dimensions larger than two, making possible their experimental demonstrations on most general systems. We propose a Bell inequali…
It is shown that the outcomes of measurements on systems in separable mixed states can be partitioned, via subsequent measurements on a disentangled extraneous system, into subensembles that display the statistics of entangled states. This motivates the introduction of the concept of "counterfactual" entanglement, which can be associated with all separable mixed states including those that are factorable. This type of entanglement gives rise to a new kind of postselection-induced Bell inequality violation. The significance of counterfactual entanglement, and its physical implications, are asse…
We study a generalization of nonlocal games---which we call extended nonlocal games---in which the players, Alice and Bob, initially share a tripartite quantum state with the referee. In such games, the winning conditions for Alice and Bob may depend on outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to randomly selected questions. Our study of this class of games was inspired by the monogamy-of-entanglement games introduced by Tomamichel, Fehr, Kaniewski, and Wehner, which they also generalize. We prove that a natur…
The direct measurement of nonlocal properties of entangled quantum systems has been the subject of several recent experimental investigations. Of particular interest is the implementation of nonlocal measurements via indirect measurement schemes, which allow for greater flexibility in the control of the measurement strength. Building on previous results established in the bipartite case, we present a scheme to implement genuine nonlocal measurements of N-qubit systems with variable strength, using GHZ-like entangled qubit meters. This method can be applied to the joint measurement of commuting…
Recently, Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] proposed the concept strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of the subsystems. As the difficulty of the problem, most of the results are restricted to tripartite systems. Here we consider a weaker form of nonlocality called local distinguishability based genuine nonlocality. A set of orthogonal multipartite quantum states is said to be genuinely nonlocal if it is locally indistinguishable for …
Two objections have been raised to the arguments presented in O. Cohen, Phys. Rev. A 60, 80 (1999). It is pointed out that neither objection has anything whatsoever to do with the main subject matter of that paper, and shown that both objections are based on misunderstandings of the examples to which they relate.
Quantum entanglement plays a central role in many areas of physics, from quantum information science to many-body systems. In order to grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of entanglement relate to each other. In 1999, Peres conjectured that Bell nonlocality is equivalent to distillability of entanglement. The intuition of Peres was that the non-classicality of an entangled state, as witnessed via Bell inequality violation, implies that pure entanglement can be distilled from this state, hence making it useful for most quantum infor…
We analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for 3-qubit pure states in the GHZ class. We consider a family of states known as the generalized GHZ states and derive an analytical expression relating the 3-tangle, which quantifies tripartite entanglement, to the Svetlichny inequality, which is a Bell-type inequality that is violated only when all three qubits are nonlocally correlated. We show that states with 3-tangle less than 1/2 do not violate the Svetlichny inequality. On the other hand, a set of states known as the maximal slice states do …
We demonstrate how to efficiently derive a broad class of inequalities for entanglement detection in multi-mode continuous variable systems. The separability conditions are established from partial transposition (PT) in combination with several distinct necessary conditions for a quantum physical state, which include previously established inequalities as special cases. Remarkably, our method enables us to support Peres' conjecture to its full generality within the framework of Cavalcanti-Foster-Reid-Drummond multipartite Bell inequality [Phys. Rev. Lett. 99}, 210405 (2007)] that the nonlocali…
The maximally entangled state can be in a mixed state as well as the well-known pure state. Taking the negativity as a measure of entanglement, we study the entanglement dynamics of bipartite, mixed maximally entangled states (MMESs) in multipartite cavity-reservoir systems. It is found that the MMES can exhibit the phenomenon of entanglement sudden death, which is quite different from the asymptotic decay of the pure-Bell-state case. We also find that maximal entanglement cannot guarantee maximal nonlocality and the MMES does not correspond to the state with maximal measurement-induced nonloc…
Motivated by Buscemi's semi-quantum nonlocal game [PRL 108, 200401(2012)], We propose an entanglement witness game, a quantum game based on entanglement witness. Similar as the semi-quantum nonlocal game, the existence of entanglement shared by the players is necessary and sufficient for obtaining a positive average payoff in our entanglement witness game. Two explicit examples are constructed to demonstrate how to play our entanglement witness game and its relations with the CHSH nonlocal game.
Recently the engineering of the entanglement for photon pairs generated during the spontaneous parametric down conversion process (SPDC) can be achieved via manipulation of pump wavelength behind a \c{hi}(2)-based type II SPDC process [1]. Such effect is used in this paper for demonstration of non-classical dispersion cancellation phenomenon in both local and nonlocal detections, theoretically. The following results are analytically achieved: I) For local detection, if narrow pump laser (highly entangled photons) are used, the dispersive broadening cancelation is directly depends on the degree…
This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication of these examples is that entanglement can profoundly affect the soundness property of two-prover interactive proof systems. We then establish limits on the probability with which strategies making use of entanglement can win restricted types of nonlocal games. These upper bounds may be regarded as gener…
We analyze entanglement and nonlocal properties of the convex set of symmetric $N$-qubits states which are diagonal in the Dicke basis. First, we demonstrate that within this set, positivity of partial transposition (PPT) is necessary and sufficient for separability --- which has also been reported recently in https://doi.org/10.1103/PhysRevA.94.060101 {Phys. Rev. A \textbf{94}, 060101(R) (2016)}. Further, we show which states among the entangled DS are nonlocal under two-body Bell inequalities. The diagonal symmetric convex set contains a simple and extended family of states that violate the …
We demonstrate an efficient experimental procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully-entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. Our method requires neither full quantum stat…
Entanglement purification is a very important element for long-distance quantum communication. Different from all the existing entanglement purification protocols (EPPs) in which two parties can only obtain some quantum systems in a mixed entangled state with a higher fidelity probabilistically by consuming quantum resources exponentially, here we present a deterministic EPP with hyperentanglement. Using this protocl, the two parties can, in principle, obtain deterministically maximally entangled pure states in polarization without destroying any less-entangled photon pair, which will improve …
Quantum entanglement and nonlocality are inextricably linked. However, while entanglement is necessary for nonlocality, it is not always sufficient in the standard Bell scenario. We derive sufficient conditions for entanglement to give rise to genuine multipartite nonlocality in networks. We find that any network where the parties are connected by bipartite pure entangled states is genuine multipartite nonlocal, independently of the amount of entanglement in the shared states and of the topology of the network. As an application of this result, we also show that all pure genuine multipartite e…
We consider unambiguous discrimination of two separable bipartite states, one being pure and the other being a rank-2 mixed state. There is a gap between the optimal success probability under global measurements and the one achieved by generalized measurements with separable measurement operators. We show that even the latter success probability cannot be achieved via local operations and classical communication, leaving a nonzero gap in between.
We present a nonlocal entanglement concentration scheme for reconstructing some maximally entangled multipartite states from partially entangled ones by exploiting cross-Kerr nonlinearities to distinguish the parity of two polarization photons. Compared with the entanglement concentration schemes based on two-particle collective unitary evolution, this scheme does not require the parties to know accurately information about the partially entangled states--i.e., their coefficients. Moreover, it does not require the parties to possess sophisticated single-photon detectors, which makes this proto…
We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell's inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process…
Relativistic causality has dramatic consequences on the measurability of nonlocal variables and poses the fundamental question of whether it is physically meaningful to speak about the value of nonlocal variables at a particular time. Recent work has shown that by weakening the role of the measurement in preparing eigenstates of the variable it is in fact possible to measure all nonlocal observables instantaneously by exploiting entanglement. However, for these measurement schemes to succeed with certainty an infinite amount of entanglement must be distributed initially and all this entangleme…
We investigate dynamical generation of macroscopic nonlocal entanglements between two remote massive magnon-superconducting-circuit hybrid systems. Two fiber-coupled microwave cavities are employed to serve as an interaction channel connecting two sets of macroscopic hybrid units each containing a magnon (hosted by a Yttrium-Iron-Garnet sphere) and a superconducting-circuit qubit. Surprisingly, it is found that stronger coupling does not necessarily mean faster entanglement generation. The proposed hybrid system allows the existence of an optimal fiber coupling strength that requests the short…
We propose an optimal nonlocal entanglement concentration protocol (ECP) for multi-photon systems in a partially entangled pure state, resorting to the projection measurement on an additional photon. One party in quantum communication first performs a parity-check measurement on her photon in an N-photon system and an additional photon, and then she projects the additional photon into an orthogonal Hilbert space for dividing the original $N$-photon systems into two groups. In the first group, the N parties will obtain a subset of $N$-photon systems in a maximally entangled state. In the second…
We report a nonlocal interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer's unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. The interferometer consists of two spatially separated balanced Mach-Zehnder or Sagnac interferometers that share a polarization entangled source. Correlations between these interferometers exhibit non-local interference, while single photon interference is suppresse…
Mixed states appear naturally in experiment over pure states. So for studying different notions of nonlocality and their relation with entanglement in realistic scenarios, one needs to consider mixed states. In a recent article [Phys. Rev. Lett. \textbf{108}, 020502 (2012)], a complete characterization of entanglement of an entire class of mixed three qubit states with the same symmetry as Greenberger-Horne-Zeilinger state known as GHZ-symmetric states, has been achieved. In this paper we investigate different notions of nonlocality of the same class of states. By finding the analytical expres…
An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication (LOCC) unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on state elimination property of the set via orthogonality-preserving measurements when all the parties a…
