We investigate whether paradigmatic measurements for quantum state tomography, namely mutually unbiased bases and symmetric informationally complete measurements, can be employed to certify quantum correlations. For this purpose, we identify a simple and noise-robust correlation witness for entanglement detection, steering and nonlocality that can be evaluated based on the outcome statistics obtained in the tomography experiment. This allows us to perform state tomography on entangled qutrits, a test of Einstein-Podolsky-Rosen steering and a Bell inequality test, all within a single experiment. We also investigate the trade-off between quantum correlations and subsets of tomographically complete measurements as well as the quantification of entanglement in the different scenarios. Finally, we perform a photonics experiment in which we demonstrate quantum correlations under these flexible assumptions, namely with both parties trusted, one party untrusted and both parties untrusted.
By combining two objects with no quantum effect one can get an object with quantum effect. Such a phenomenon, often referred to as activation has been analyzed for the notion of steering nonlocality. Activation of steering nonlocality is observed for different classes of mixed entangled states in linear network scenarios. Characterization of arbitrary two qubit states, in ambit of steering activation in network scenarios has been provided in this context. Using the notion of reduced steering, instances of steerability activation are also observed in nonlinear network. Present analysis involves…
Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is corres…
The certification of Bell nonlocality or quantum steering implies the use of incompatible measurements. Here we make this connection quantitative. We show how to strengthen robustness-based steering and nonlocality quantifiers in order that they give strong lower bounds to previously proposed incompatibility quantifiers. Our results can be seen from two perspectives. On the one hand, they can be used to estimate how much steering or nonlocality can be demonstrated with a given set of measurements. On the other hand, they gives one-sided device-independent and device-independent ways of estimat…
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…
Recently quantum nonlocality has been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell's nonlocality. Among which, Bell's nonlocality is the strongest type. Bell's nonlocality for quantum states is usually detected by violation of some Bell's inequalities, such as Clause-Horne-Shimony-Holt inequality for two qubits. Steering is a manifestation of nonlocality intermediate between entanglement and Bell's nonlocality. This peculiar feature has led to a curious quantum phenomenon, the one-way Einstein-Podolsky-Rosen steering. The one-way steeri…
We derive general conditions for the compatibility of channels in general probabilistic theory. We introduce formalism that allows us to easily formulate steering by channels and Bell nonlocality of channels as generalizations of the well-known concepts of steering by measurements and Bell nonlocality of measurements. The generalization does not follow the standard line of thinking stemming from the Einstein-Podolsky-Rosen paradox, but introduces steering and Bell nonlocality as entanglement-assisted incompatibility tests. We show that all of the proposed definitions are, in the special case o…
The celebrated Einstein-Podolsky-Rosen quantum steering has a complex structure in the multipartite scenario. We show that a naively defined criterion for multipartite steering allows, like in Bell nonlocality, for a contradictory effect whereby local operations could create steering seemingly from scratch. Nevertheless, neither in steering nor in Bell nonlocality has this effect been experimentally confirmed. Operational consistency is reestablished by presenting a suitable redefinition: there is a subtle form of steering already present at the start, and it is only exposed -- as opposed to c…
Quantum nonlocality and quantum steering are fundamental correlations of quantum systems which can not be created using classical resources only. Nonlocality describes the ability to influence the possible results of measurements carried out in distant systems, in quantum steering Alice remotely steers Bob's state. Research in nonlocality and steering possess a fundamental interest for the development of quantum information and in many applications requiring nonlocal resources like quantum key distribution. On the other hand, the Stern-Gerlach experiment holds an important place in the history…
The concept of steering was introduced by Schrodinger in 1935 as a generalization of the EPR paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and Isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell-nonlocality. …
This paper illustrates a direct connection between quantum steering and non-trivial preparation contextuality. In two party-two measurement per party-two outcomes per measurement $(2-2-2)$ Bell scenario, any argument of Bell nonlocality is a proof of trivial preparation contextuality; however, the converse may not hold. If one of the parties (say, Alice) performs the measurements of more than two dichotomic observables, then it is possible to find a set of non-trivial functional relations between Alice's observables. We argue that the existence of a suitable set of such non-trivial relations b…
Generalized quantum discord $(D_q)$, Einstein-Podolsky-Rosen steering $(S)$, entanglement $(E)$, and Bell nonlocality ($N$), are logically distinct quantifiers of quantum correlations. All these measures capture nonclassical aspects of quantum states and play some role as resources in quantum information processing. In this work, we look for the hierarchy satisfied by these quantum correlation witnesses for a class of two-qubit states. We show that $N \triangleright S\triangleright E\triangleright D_q$, meaning that nonlocality implies steering, which in turn implies entanglement, which then i…
Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set …
In a recent work [Phys. Rev. Lett. {\bf 98}, 140402 (2007)] we defined ``steering'', a type of quantum nonlocality that is logically distinct from both nonseparability and Bell-nonlocality. In the bipartite setting, it hinges on the question of whether Alice can affect Bob's state at a distance through her choice of measurement. More precisely and operationally, it hinges on the question of whether Alice, with classical communication, can convince Bob that they share an entangled state, under the circumstances that Bob trusts nothing that Alice says. We argue that if she can, then this demonst…
We investigate under which conditions quantum nonlocal manifestations as Einstein-Podolsky-Rosen steering or Bell nonlocality can manifest themselves even at the macroscopic level of two mechanical resonators in optomechanical systems. We adopt the powerful scheme of reservoir engineering, implemented by driving a cavity mode with a properly chosen two-tone field, to prepare two mechanical oscillators into an entangled state. We show that large and robust (both one-way and two-way) steering could be achieved in the steady state with realistic parameters. We analyze the mechanism of the asymmet…
The discovery of postquantum nonlocality, i.e., the existence of nonlocal correlations that are stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations of quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While postquantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that postquantum …
In this paper, we investigate the dynamics behaviors of genuine multipartite Einstein-Podolsky-Rosen steering (GMS) and genuine multipartite nonlocality (GMN), and explore how to recover the lost GMS and GMN under a mixed decoherence system. Explicitly, the decoherence system can be modeled by that a tripartite Werner-type state suffers from the non-Markovian regimes and one subsystem of the tripartite is under a non-inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner-type state established initially. GMS and GMN are very fragi…
In this work, there are two parties, Alice on Earth and Bob on the satellite, which initially share an entangled state, and some open problems, which emerge during quantum steering that Alice remotely steers Bob, are investigated. Our analytical results indicate that all entangled pure states and maximally entangled evolution states (EESs) are steerable, and not every entangled evolution state is steerable and some steerable states are only locally correlated. Besides, quantum steering from Alice to Bob experiences a "sudden death" with increasing decoherence strength. However, shortly after t…
Quantum steering refers to correlations that can be classified as intermediate between entanglement and Bell nonlocality. Every state exhibiting Bell nonlocality exhibits also quantum steering and every state exhibiting quantum steering is also entangled. In low dimensional cases similar hierarchical relations have been observed between the temporal counterparts of these correlations. Here, we study the hierarchy of such temporal correlations for a general multilevel quantum system. We demonstrate that the same hierarchy holds for two definitions of state over time. In order to compare differe…
Quantum steering, loosely speaking the distribution of entanglement from an untrusted party, is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. Determining which states can be steered is important from a conceptual point of view, but also for applications, e.g. in quantum cryptography. Here we show that bound entanglement, although it represents the weakest form of entanglement, can nevertheless lead to quantum steering. This is done by noticing that steering inequalities can be derived from entropic uncertainty relations. Our result has implicati…
Genuine steering is still not well understood enough in contrast to genuine entanglement and nonlocality. Here we provide a protocol which can reveal genuine steering under some restricted operations compared to the existing witnesses of genuine multipartite steering. Our method has an impression of some sort of hidden protocol in the same spirit of hidden nonlocality, which is well understood in bipartite scenario. We also introduce a genuine steering measure which indicates the enhancement of genuine steering in the final state of our protocol compared to the initial states.
The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it…
Entanglement, quantum steering and nonlocality are distinct quantum correlations which are the resources behind various of quantum information and quantum computation applications. However, a central question of determining the precise quantitative relation among them is still unresolved. Here, we present a mapping criterion between Bell nonlocality and quantum steering in bipartite qudit-qubit system, as well as a mapping criterion between quantum steering and quantum entanglement in bipartite qubit-qudit system, starting from the fundamental concepts of quantum correlations. Precise quantita…
A single photon, delocalized over two optical modes, is characterized by means of quantum homodyne tomography. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical quantum bit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments.
The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show h…
We develop criteria to detect three classes of nonlocality that have been shown by Wiseman et al. [Phys. Rev. Lett. 98, 140402 (2007)] to be nonequivalent: entanglement, EPR steering, and the failure of local hidden-variable theories. We use the approach of Cavalcanti et al. [Phys. Rev. Lett. 99, 210405 (2007)] for continuous variables to develop the nonlocality criteria for arbitrary spin observables defined on a discrete Hilbert space. The criteria thus apply to multisite qudits, i.e., systems of fixed dimension d, and take the form of inequalities. We find that the spin moment inequalities …
Einstein-Podolsky-Rosen steering is a form of quantum nonlocality intermediate between entanglement and Bell nonlocality. Although Schrödinger already mooted the idea in 1935, steering still defies a complete understanding. In analogy to "all-versus-nothing" proofs of Bell nonlocality, here we present a proof of steering without inequalities rendering the detection of correlations leading to a violation of steering inequalities unnecessary. We show that, given any two-qubit entangled state, the existence of certain projective measurement by Alice so that Bob's normalized conditional states can…
Protocols for testing or exploiting quantum correlations-such as entanglement, Bell nonlocality, and Einstein-Podolsky-Rosen steering- generally assume a common reference frame between two parties. Establishing such a frame is resource-intensive, and can be technically demanding for distant parties. While Bell nonlocality can be demonstrated with high probability for a large class of two-qubit entangled states when the parties have one or no shared reference direction, the degree of observed nonlocality is measurement-orientation dependent and can be arbitrarily small. In contrast, we theoreti…
We formally link the concept of steering (a concept created by Schrodinger but only recently formalised by Wiseman, Jones and Doherty [Phys. Rev. Lett. 98, 140402 (2007)] and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A, 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variables observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-ty…
For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein-Podolsky-Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell-nonlocality.
Einstein-Podolsky-Rosen steering is a form of quantum nonlocality which is weaker than Bell nonlocality, but stronger than entanglement. Here we present a method to check Einstein-Podolsky-Rosen steering in the scenario where the steering party performs two black-box measurements and the trusted party performs projective qubit measurements corresponding to two arbitrary mutually unbiased bases. This method is based on decomposing the measurement correlations in terms of extremal boxes of the steering scenario. In this context, we propose a measure of steerability called steering cost. We show …
Einstein-Podolsky-Rosen steering describes a quantum correlation in addition to entanglement and Bell nonlocality. However, conceptually different from entanglement and Bell nonlocality, quantum steering has an asymmetric definition. Motivated by the asymmetric definition of quantum steering, we study the steerability of two-interacting qubits, which have asymmetric energy levels, coupled with asymmetric environments. The asymmetric (nonequilibrium) environments are two environments with different temperatures or chemical potentials. The Bloch-Redfield equation is applied to study the dynamics…
Bell nonlocality between distant quantum systems---i.e., joint correlations which violate a Bell inequality---can be verified without trusting the measurement devices used, nor those performing the measurements. This leads to unconditionally secure protocols for quantum information tasks such as cryptographic key distribution. However, complete verification of Bell nonlocality requires high detection efficiencies, and is not robust to the typical transmission losses that occur in long distance applications. In contrast, quantum steering, a weaker form of quantum correlation, can be verified fo…
In this paper, we propose a continuous measurement and feedback scheme to achieve strong Einstein-Podolsky-Rosen (EPR) steering and Bell nonlocality of two macroscopic mechanical oscillators in cavity optomechanics. Our system consists of two optomechanical cavities in which two cavity fields are coupled to each other via a nondegenerate parametric downconversion. The two cavity output fields are subject to continuous Bell-like homodyne detection and the detection currents are fed back to drive the cavity fields. It is found that when the feedback is absent, the two mechanical oscillators can …
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…
A single photon incident on a beam splitter produces an entangled field state, and in principle could be used to violate a Bell-inequality, but such an experiment (without post-selection) is beyond the reach of current experiments. Here we consider the somewhat simpler task of demonstrating EPR-steering with a single photon (also without post-selection). That is, of demonstrating that Alice's choice of measurement on her "half" of a single photon can affect the other "half" of the photon in Bob's lab, in a sense rigorously defined by us and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]. Previou…
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR-steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, t…
Einstein-Podolsky-Rosen (EPR) steering exhibits an inherent asymmetric feature that differs from both entanglement and Bell nonlocality, which leads to one-way EPR steering. Although this one-way EPR steering phenomenon has been experimentally observed, the schemes to manipulate the direction of EPR steering have not been investigated thoroughly. In this paper, we propose and experimentally demonstrate three schemes to manipulate the direction of EPR steering, either by varying the noise on one party of a two-mode squeezed state (TMSS) or transmitting the TMSS in a noisy channel. The dependenc…
The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bob's system, are: (i) one where Bob also has an input and operates on his subsystem, and (ii) the `instrumental steering' scenario. We show that such bipartite post-quantum steeri…
We study multipartite Bell nonlocality in a framework native of multipartite Einstein-Podolsky-Rosen (EPR) steering scenarios with a single trusted measurement device. We derive a closed-form necessary and sufficient criterion for systems composed of a qubit and N-1 untrusted black-box measurement devices to violate -- under general dichotomic measurements on the qubit -- a generic Bell inequality from a broad family of linear inequalities with arbitrarily many outputs for the N-1 untrusted devices and inputs for all N parties. The optimal quantum measurements for maximal violation are also ob…
Within the hierarchy of inseparable quantum correlations, Einstein-Podolsky-Rosen steering is distinguished from both entanglement and Bell nonlocality by its asymmetry -- there exist conditions where the steering phenomenon changes from being observable to not observable, simply by exchanging the role of the two measuring parties. Whilst this one-way steering feature has been previously demonstrated for the restricted class of Gaussian measurements, for the general case of positive-operator-valued measures even its theoretical existence has only recently been settled. Here, we prove, and then…
In [\href{http://www.sciencedirect.com/science/article/pii/037596019290711T}{Phys. Lett. A {\bf 166}, 293 (1992)}] Popescu characterized nonlocality of pure $n$-partite entangled systems by studying bipartite violation of local realism when $n-2$ number of parties perform projective measurements on their particles. A pertinent question in this scenario is whether similar characterization is possible for $n$-partite mixed entangled states also. In the present work we have followed an analogous approach so as to explore whether given a tripartite mixed entangled state the conditional bipartite s…
The Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum nonlocality between entanglement and Bell nonlocality, which plays an important role in quantum information processing tasks. In the past few years, the investigations concerning EPR steering have been demonstrated in a series of experiments. However, these studies rely on the relevant steering inequalities and the choices of measurement settings. Here, we experimentally verify the EPR steering via entanglement detection without using any steering inequality and measurement setting. By constructing two new states from a two-…
We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hi…
We examine Einstein-Podolsky-Rosen's (EPR) steering nonlocality for two realisable Schrodinger cat-type states where a meso/ macroscopic system (called the "cat"-system) is entangled with a spin-$1/2$ system. For large cat-systems, we show that a local hidden state model is near-satisfied, meaning that the cat-system can be consistent with being in a mixture of "dead" and "alive" states despite that it is entangled with the spin system. We justify that a rigorous signature of the Schrodinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This le…
Quantum nonlocality is a kind of significant quantum correlation that is stronger than quantum entanglement and EPR steering. The standard tripartite nonlocality can be detected by the violation of the Mermin inequality. By using local filtering operations, we give a tight upper bound on the maximal expected value of the Mermin operators. By detailed examples we show that the hidden standard nonlocality can be revealed by local filtering which can enhance the robustness of the noised entangled states.
We investigate the complexity cost of demonstrating the key types of nonclassical correlations --- Bell inequality violation, EPR-steering, and entanglement --- with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently-discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known CHSH test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require non-projective measuremen…
We present a tomographic approach to the study of quantum nonlocality in multipartite systems. Bell inequalities for tomograms belonging to a generic tomographic scheme are derived by exploiting tools from convex geometry. Then, possible violations of these inequalities are discussed in specific tomographic realizations providing some explicit examples.
The Einstein-Podolsky-Rosen (EPR) paradox established a link between entanglement and nonlocality in quantum mechanics. EPR steering is the nonlocality associated with the EPR paradox and has traditionally only been investigated between two parties. Here, we present the first experimental observations of multipartite EPR steering, and of the genuine tripartite continuous variable entanglement of three mesoscopic optical systems. We explore different linear optics networks - each one with optimised asymmetries - that create multipartite steerable states containing different numbers of quantised…
