Quantum steering in a system consisting of a qubit coupled to a single-mode field is explored when classical-like measurements implemented by heterodyne detection schemes that collapse the state of the field on to a coherent state is considered. The quantum steering ellipsoid of the qubit is constructed to visualize the set of states on to which it can be steered using such measurements. In some cases, the steering set does not form an ellipsoid since only heterodyne detection is considered. Evolution of the steering ellipsoid corresponding to joint evolution of the qubit and field under the Jaynes-Cummins hamiltonian is also studied.
We consider the Cavalcanti-Foster-Fuwa-Wiseman inequality~\cite{achsh} which is a necessary and sufficient steerability condition for two-qubit states with two measurement settings on each side. We derive the criterion which an arbitrary two-qubit state must satisfy in order to violate this inequality, and obtain its maximum attainable violation in quantum mechanics. The derived condition on the state parameters enables us to establish a tight monogamy relation for two-qubit steering.
EPR steering is an important quantum resource in quantum information and computation. In this paper, its applications in quantum teleportation are investigated. First of all, the upper bound of the average teleportation fidelity based on the EPR steering is derived. When the receiver can only perform the identity or the Pauli rotation operations, the X-type states which violate the three-setting linear steering inequality could be used for teleportation. In the end, the steering observables and the average teleportation fidelities of the two-qubit reduced states for three-qubit pure states mai…
We identify the families of states that maximise some recently proposed quantifiers of Einstein-Podolsky-Rosen (EPR) steering and the volume of the Quantum Steering Ellipsoid (QSE). The optimal measurements which maximise genuine EPR steering measures are discussed and we develop a novel way to find them using the QSE. We thus explore the links between genuine EPR steering and the QSE and introduce states that can be the most useful for one-sided device-independent quantum cryptography for a given amount of noise.
By employing Pauli measurements, we present some nonlinear steering criteria applicable for arbitrary two-qubit quantum systems and optimized ones for symmetric quantum states. These criteria provide sufficient conditions to witness steering, which can recover the previous elegant results for some well-known states. Compared with the existing linear steering criterion and entropic criterion, ours can certify more steerable states without selecting measurement settings or correlation weights, which can also be used to verify entanglement as all steerable quantum states are entangled.
The present work is motivated by the question as to what aspect of correlation entailed by the two-qubit state serves as the appropriate quantitative resource for steering. To this end, considering Bell-diagonal states, suitable measures of simultaneous correlations in two and three complementary (mutually unbiased) bases are identified as the relevant resources for quantum steering. Quantitative relations between appropriate measures of quantum steering and the corresponding measures of simultaneous correlations in complementary bases are demonstrated which ensure that for two qubit steerable…
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one party to remotely affect another's state through local measurements. One of the most distinguishable properties of EPR steering is its asymmetric aspect. Steering can work in one direction but fail in the opposite direction. This type of one-way steering, which is different from the symmetry concepts of entanglement and Bell nonlocality, has garnered much interest. However, an experimental demonstration of genuine EPR steering in the simplest scenario, i.e., one that employs two-qubit systems, is still lacking. In this work, w…
In the last few years, several criteria to identify Eistein-Podolski-Rosen steering have been proposed and experimentally implemented. On the operational side, however, the evaluation of the steerability degree of a given state has shown to be a difficult task and only a few results are known. In this work, we propose a measure of steering that is based on the maximal violation of well established steering inequalities. Applying this approach to two-qubit states, we managed to derive simple closed formulas for steering in the two- and three-measurement scenarios. Among the options investigated…
In the present work, we address the question of how bipartite steering violation takes place among multi-partite systems (where each sub-system have Hilbert space dimension restricted to two) based on the maximal violations of the bipartite steering inequality of the reduced pairwise qubit systems. We have derived a trade-off relation which is satisfied by those pairwise bipartite maximal steering violations, which physically can be understood as providing restrictions on the distribution of steering among subsystems. For a three-qubit system, it is impossible that all pairs of qubits violate …
Quantum steering has been exploited as an important resource in modern quantum information processing. Owing to its directional nature, some quantum states that are asymmetric under the exchange of parties have been found to manifest steering only in specific direction, thus called one-way steering. Existing works focused on one-way steering in systems of qubits. Here we propose a family of two-party states that are one-way steerable in systems of $d$-dimension. In particular, we validate the one-way steerability of the states for $d=3$, and demonstrate how one-way steering parameter space man…
When two qubits A and B are in an appropriate state, Alice can remotely steer Bob's system B into different ensembles by making different measurements on A. This famous phenomenon is known as quantum steering, or Einstein-Podolsky-Rosen steering. Importantly, quantum steering establishes the correspondence not only between a measurement on A (made by Alice) and an ensemble of B (owned by Bob) but also between each of Alice's measurement outcomes and an unnormalized conditional state of Bob's system. The unnormalized conditional states of B corresponding to all possible measurement outcomes of …
According to the geometric characterization of measurement assemblages and local hidden state (LHS) models, we propose a steering criterion which is both necessary and sufficient for two-qubit states under arbitrary measurement sets. A quantity is introduced to describe the required local resources to reconstruct a measurement assemblage for two-qubit states. We show that the quantity can be regarded as a quantification of steerability and be used to find out optimal LHS models. Finally we propose a method to generate unsteerable states, and construct some two-qubit states which are entangled …
Entangled two-qubit states are the core building blocks for constructing quantum communication networks. Their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. In this work we study the self-testing of two-qubit entangled states via steering inequalities, with robustness analysis against noise. More precisely, steering inequalities are constructed from the tilted Clauser-Horne-Shimony-Holt inequality and its general form, to verify the general two-qubit entangled states. The study provides a good robustness bound, using both local extracti…
The quantum steering ellipsoid can be used to visualise two-qubit states, and thus provides a generalisation of the Bloch picture for the single qubit. Recently, a monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit states and shown to be stronger than the celebrated Coffman-Kundu-Wootters (CKW) inequality. We first demonstrate the close connection between this volume monogamy relation and the classification of pure 3-qubit states under stochastic local operations and classical communication (SLOCC). We then show that this monogamy relation does not hold …
Einstein-Podolsky-Rosen (EPR) steering is the ability that an observer persuades a distant observer to share entanglement by making local measurements. Determining a quantum state is steerable or unsteerable remains an open problem. Here, we derive a new steering inequality with infinite measurements corresponding to an arbitrary two-qubit T state, from consideration of EPR steering inequalities with N projective measurement settings for each side. In fact, the steering inequality is also a sufficient criterion for guaranteering that the T state is unsteerable. Hence, the steering inequality c…
Einstein-Podolsky-Rosen (EPR) steering allows Alice to remotely prepare a state in some specific bases for Bob through her choice of measurements. The temporal analogue of EPR steering, temporal steering, also reveals the steerability of a single system between different times. Focusing on a four-dimensional system, here we investigate the dynamics of the temporal steering measures, the temporal steering robustness, using 5 mutually unbiased bases. As an example of an application, we use these measures to examine the temporal correlations in a radical pair model of magnetoreception. We find th…
It has been shown in earlier works that the vertices of Platonic solids are good measurement choices for tests of EPR-steering using isotropically entangled pairs of qubits. Such measurements are regularly spaced, and measurement diversity is a good feature for making EPR-steering inequalities easier to violate in the presence of experimental imperfections. However, such measurements are provably suboptimal. Here, we develop a method for devising optimal strategies for tests of EPR-steering, in the sense of being most robust to mixture and inefficiency (while still closing the detection loopho…
We investigate quantum steering of an open quantum system by measurements on its environment in the framework of collision models. As an example we consider a coherently driven qubit dissipatively coupled to a bath. We construct local non-adaptive and adaptive as well as nonlocal measurement scenarios specifying explicitly the measured observable on the environment. Our approach shows transparently how the conditional evolution of the open system depends on the type of the measurement scenario and the measured observables. These can then be optimized for steering. The nonlocal measurement scen…
The demonstration of quantum teleportation of a photonic qubit from Alice to Bob usually relies on data conditioned on detection at Bob's location. I show that Bohm's Einstein-Podolsky-Rosen (EPR) paradox can be used to verify that the quantum benchmark for qubit teleportation has been reached, without postselection. This is possible for scenarios insensitive to losses at the generation station, and with efficiencies of $η_{B}>1/3$ for the teleportation process. The benchmark is obtained, if it is shown that Bob can {}"steer" Alice's record of the qubit as stored by Charlie. EPR steering inequ…
Superconducting qubits with tunable coupling are ideally suited for fast and accurate implementation of quantum logic. Here we present a simple approach, based on Weyl chamber steering, to CNOT gate design for inductively coupled phase qubits with tunable coupling strength g. In the presence of simultaneous rf pulses on the individual qubits that appropriately track the coupling strength as it is varied, we show that an infinite family of switching sequences preserving the time integral or "area" of g can be used to generate CNOT logic. We demonstrate our approach by considering time-dependenc…
Adopting the geometric description of steering assemblages and local hidden states (LHS) model, we construct the optimal LHS model for some two-qubit states under continuous projective measurements, and obtain a sufficient steering criterion for all two-qubit states. Using the criterion, we show more two-qubit states that are asymmetric in steering scenario under projective measurements. Then we generalize the geometric description into higher dimensional bipartite cases, calculate the steering bound of two-qutrit isotropic states and make discussion on more general cases.
We investigate the possibility of multiple use of a single copy of three-qubit states for genuine tripartite Einstein-Podolsky-Rosen (EPR) steering. A pure three-qubit state of either the Greenberger-Horne-Zeilinger (GHZ)-type or W-type is shared between two fixed observers in two wings and a sequence of multiple observers in the third wing who perform unsharp or non-projective measurements. The choice of measurement settings for each of the multiple observers in the third wing is independent and uncorrelated with the measurement settings and outcomes of the previous observers. We investigate …
We consider the problem of $1$-sided device-independent self-testing of any pure entangled two-qubit state based on steering inequalities which certify the presence of quantum steering. In particular, we note that in the $2-2-2$ steering scenario (involving $2$ parties, $2$ measurement settings per party, $2$ outcomes per measurement setting), the maximal violation of a fine-grained steering inequality can be used to witness certain extremal steerable correlations, which certify all pure two-qubit entangled states. We demonstrate that the violation of analogous CHSH inequality of steering or n…
Quantum steering, a type of quantum correlation with unique asymmetry, has important applications in asymmetric quantum information tasks. We consider a new quantum steering scenario in which one half of a two-qubit Werner state is sequentially measured by multiple Alices and the other half by multiple Bobs. We find that the maximum number of Alices who can share steering with a single Bob increases from 2 to 5 when the number of measurement settings $N$ increases from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a fixed $N$, at most 2 Alices can share steering with 2 B…
Einstein-Podolsky-Rosen steering refers to the quantum phenomenon whereby the state of a system held by one party can be "steered" into different states at the will of another, distant, party by performing different local measurements. Although steering has been demonstrated in a number of experiments involving qubits, the question of which two-qubit states are steerable remains an open theoretical problem. Here, we derive a necessary condition for any two-qubit state to be steerable when the steering party suffers from a given probability of qubit loss. Our main result finds application in on…
In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of nonorthogonal quantum states. In this Letter, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental…
The bidirectional steerability between different-size subsystems is discussed for a single parameter accelerated qubit-qutrit system. The decoherence due to the mixing and acceleration parameters is investigated, where for the total system and the qutrit, it increases as the mixing parameter increases, while it decreases for the qubit. The non-classical correlations are quantified by using the local quantum uncertainty, where it increases at large values of the acceleration parameter. The possibility that each subsystem steers each other is studied, where the behavior of the steering inequalit…
An experimental proposal certification for any three-qubit generalized Greenberger-Horne-Zeilinger states based on the fine-grained steering inequality
Quantum Steering vs Entanglement and Extracting Work in an Anisotropic Two-Qubit Heisenberg Model in Presence of External Magnetic Fields with DM and KSEA Interactions
Quantum steering can be detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Here we discuss the converse problem, namely ensuring that a state is unsteerable, and hence Bell local. We present a simple criterion, applicable to any two-qubit state, which guarantees that the state admits a local hidden state model for arbitrary projective measurements. We find new classes of unsteerable entangled states, which can thus not violate any steering or Bell inequality. In turn, this leads to sufficient conditions for a state t…
The behaviour of genuine EPR steering of three qubit states under various environmental noises is investigated. In particular, we consider the two possible steering scenarios in the tripartite setting: (1 -> 2), where Alice demonstrates genuine steering to Bob-Charlie, and (2 -> 1), where Alice-Bob together demonstrates genuine steering to Charlie. In both these scenarios, we analyze the genuine steerability of the generalized Greenberger-Horne-Zeilinger (gGHZ) states or the W-class states under the action of noise modeled by amplitude damping (AD), phase flip (PF), bit flip (BF), and phase da…
The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid---called the quantum steering ellipsoid---in the Bloch ball. This ellipsoid provides a simple visual characterisation of the initial 2-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarisation-entangled photonic qubit states. Moreover, for pure 3-qubit states, the volumes of the two quantum steering ellipsoids generated by measurements on the first qu…
Quantum steering is an important nonclassical resource for quantum information processing. However, even lots of steering criteria exist, it is still very difficult to efficiently determine whether an arbitrary two-qubit state shared by Alice and Bob is steerable or not, because the optimal measurement directions of Alice are unknown. In this work, we provide an efficient quantum steering detection scheme for arbitrary 2-qubit states with the help of machine learning, where Alice and Bob only need to measure in a few fixed measurement directions. In order to prove the validity of this method, …
Recently, a connection between quantum coherence and quantum steering was established and criteria for quantum steering or in other words, nonlocal advantage of quantum coherence (NAQC) were derived for two-qubit states. Here, we derive a set of complementarity relations between the steering or NAQC inequalities achieved by various criteria. We also extend the idea in the multi-partite scenario, specifically, in the three-qubit scenario, which can easily be generalized to the multi-partite scenario.
The effect of a local trace-preserving single-qubit channel on a two-qubit state is investigated in the picture of the quantum steering ellipsoids (QSE). The phenomenon of locally increased quantum correlation is visualized in this picture. We strictly prove that a $B$-side two-qubit discordant state can be locally prepared from a classical state by a trace-preserving channel on qubit $B$ if and only if its QSE of $B$ is a non-radial line segment. For states with higer-dimensional QSEs, the phenomenon of locally increased quantum correlation generally happens when the shape of the QSE is like …
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…
EPR-steering refers to the ability of one observer to convince a distant observer that they share entanglement by making local measurements. Determining which states allow a demonstration of EPR-steering remains an open problem in general. Here, we outline and demonstrate a method of analytically constructing new classes of two-qubit states which are non-steerable by arbitrary projective measurements, from consideration of local operations performed by the steering party on states known to be non-steerable.
We demonstrate how quantum optimal control can be used to enhance quantum resources for bipartite one-way protocols, specifically EPR-steering with qubit measurements. Steering is relevant for one-sided device-independent key distribution, the realistic implementations of which necessitate the study of noisy scenarios. So far mainly the case of imperfect detection efficiency has been considered; here we look at the effect of dynamical noise responsible for decoherence and dissipation. In order to set up the optimisation, we map the steering problem into the equivalent joint measurability probl…
We study the Einstein-Podolsky-Rosen (EPR) steering and present steerability criteria for arbitrary qubit-qudit (qudit-qubit) systems based on mutually unbiased measurements (MUMs) and general symmetric informationally complete measurements (general SIC-POVMs). Avoiding the usual complicated steering inequalities, these criteria can be more operational than some existing criteria and implemented experimentally. Detailed examples are given to illustrate the efficiency of the criteria in both computation and experimental implementation.
We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated…
The quantum steering ellipsoid of a two-qubit state is the set of Bloch vectors that Bob can collapse Alice's qubit to, considering all possible measurements on his qubit. We provide an elementary construction of the ellipsoid for arbitrary states, calculate its volume, and explain how this geometric representation can be made faithful. The representation provides a range of new results, and uncovers new features, such as the existence of "incomplete steering" in separable states. We show that entanglement can be analysed in terms of three geometric features of the ellipsoid, and prove that a …
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…
Fully characterizing the steerability of a quantum state of a bipartite system has remained an open problem since the concept of steerability was defined. In this work, using our recent geometrical approach to steerability, we suggest a necessary and sufficient condition for a two-qubit state to be steerable with respect to projective measurements. To this end, we define the critical radius of local models and show that a state of two qubits is steerable with respect to projective measurements from Alice's side if and only if her critical radius of local models is less than $1$. As an example,…
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…
Quantum steering is a recently-defined form of quantum correlation which lies at the heart of quantum mechanics. In difference from other types of quantum correlations, quantum steering is inherently asymmetric, which implies that it could manifest in one direction but not in the opposite direction. This rather peculiar phenomenon, known as one-way steering, have been demonstrated in several experiments, but subtlety remains. In fact all experiments were shown to be ambiguous until a very recent conclusive one, which however made a crucial use of a high dimensional embedding to get around assu…
The steering property known for two qubit-state in terms of specific inequalities for correlation function is translated for the state of qudit with the spin $j=3/2$. Since most steering detection inequalities are based on the correlation functions we introduce analogs of such functions for the single qudit systems. The tomographic probability representation for the qudit states is applied. The connection between the correlation function in two qubit system and the single qudit is presented in an integral form with a intertwining kernel calculated explicitly in tomographic probability terms.
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 inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states are shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present study we propose a new criteria to dete…
We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of one-qubit operations can be transformed into a steering problem on the Bloch sphere, whereas the two-qubit problem can be generally transformed into a steering problem in a tetrahedron representing all the local equivalence classes of two-qubit operations (the Weyl chamber). We use this approach to investigate several physical examples for the generation of two-qubit…
The question of which two-qubit states are steerable (i.e. permit a demonstration of EPR-steering) remains open. Here, a strong necessary condition is obtained for the steerability of two-qubit states having maximally-mixed reduced states, via the construction of local hidden state models. It is conjectured that this condition is in fact sufficient. Two provably sufficient conditions are also obtained, via asymmetric EPR-steering inequalities. Our work uses ideas from the quantum steering ellipsoid formalism, and explicitly evaluates the integral of $\boldsymbol n/(\boldsymbol n^\intercal A\bo…
