Quantum steering is a perplexing feature at the heart of quantum mechanics that provides profound implications in understanding the nature of physical reality. On the other hand, the effect of relativistic features on quantum systems is vital in understanding the underlying foundations of physics. In this work, we study the effects of Unruh acceleration on the quantum steering of a two-qubit system. In particular, we consider the so-called quantum steering ellipsoid and the maximally-steered coherence in a non-inertial frame and find closed-form analytic expressions for the role of the Unruh acceleration in these quantities. Analyzing the conditions for the steerability of the system, we develop a geometric description for the effect of Unruh acceleration on the quantum steering of a two-qubit system.
Quantum steering is a perplexing feature at the heart of quantum mechanics that provides profound implications in understanding the nature of physical reality. On the other hand, the effect of relativistic features on quantum systems is vital in understanding the underlying foundations of physics. In this work, we study the effects of Unruh acceleration on the quantum steering of a two-qubit system. In particular, we consider the so-called quantum steering ellipsoid and the maximally-steered coherence in a non-inertial frame and find closed-form analytic expressions for the role of the Unruh acceleration in these quantities. Analyzing the conditions for the steerability of the system, we develop a geometric description for the effect of Unruh acceleration on the quantum steering of a two-qubit system.
We investigate directional quantum steering harvesting by two uniformly accelerated non-identical Unruh-DeWitt detectors coupled to a massless scalar field in the Minkowski vacuum. We show that the Unruh effect does not simply degrade harvested steering, but can reshape its directionality in a strongly parameter-dependent manner. At low detector energy scales, acceleration predominantly suppresses steering, whereas at higher energy scales, moderate acceleration can enhance steering and even activate an initially absent steering direction. Most strikingly, within a finite acceleration window, the Unruh effect enhances steering in one direction while simultaneously suppressing it in the opposite direction, revealing an intrinsically directional influence of relativistic acceleration. Detector non-identicality provides an additional control mechanism: a moderate energy-gap mismatch can enhance or activate one steering direction while suppressing the reverse one, whereas sufficiently large energy-gap mismatch suppresses the harvested steering. Moreover, the maximal steering asymmetry approximately marks the transition from two-way to one-way steering. Our results establish relativistic acceleration and detector non-identicality as means of controlling the strength and directionality of vacuum-harvested quantum correlations.
Graphical representations are invaluable for visualising physical systems and processes. In quantum information theory, the Bloch vector representation of a single qubit is ubiquitous, but visualising higher-dimensional quantum systems is far less straightforward. The quantum steering ellipsoid provides a method for geometrically representing the state of two qubits, the most fundamental system for studying quantum correlations. This thesis constitutes a significant development of the steering ellipsoid formalism. As well as offering new insight into the study of two-qubit states, we extend this powerful geometric approach to explore scenarios beyond two qubits. We find necessary and sufficient conditions for when an ellipsoid inside the Bloch ball describes a valid (i.e. positive semidefinite) two-qubit state. Combined with the notion of ellipsoid chirality, this enables a geometric characterisation of entanglement. We find a family of "maximally obese" two-qubit states whose ellipsoids have maximal volume. These states have optimal correlation properties within the set of all two-qubit states with a single maximally mixed marginal. We study a three-qubit scenario and discover that ellipsoid volume obeys an elegant monogamy of steering relationship. From this we can derive the Coffman-Kundu-Wootters (CKW) inequality for concurrence monogamy, providing an intuitive geometric derivation of this classic result. Remarkably, we find that steering ellipsoids offer a fresh perspective on questions beyond quantum state space. Entanglement witnesses are also very naturally represented and classified using the formalism. This gives a physical interpretation to any ellipsoid inside the Bloch ball as a block positive two-qubit operator, which we may then classify further. We can also use steering ellipsoids to derive some highly nontrivial results in classical Euclidean geometry, extending Euler's inequality for the circumradius and inradius of a triangle.
Abstract Quantum coherence, a fundamental aspect of quantum mechanics, plays a crucial role in various quantum information tasks. However, preserving coherence under extreme conditions, such as relativistic acceleration, poses significant challenges. In this paper, we investigate the influence of Unruh temperature and energy levels on the evolution of maximal steered coherence (MSC) for different initial states. Our results reveal that MSC is strongly dependent on Unruh temperature, exhibiting behaviors ranging from monotonic decline to non-monotonic recovery, depending on the initial state parameter Δ0 Δ 0 . Notably, when Δ0=1 Δ 0 = 1 , MSC is generated as Unruh temperature increases. Additionally, we observe that higher energy levels help preserve or enhance MSC in the presence of Unruh effects. These findings offer valuable insights into the intricate relationship between relativistic effects and quantum coherence, with potential applications in developing robust quantum technologies for non-inertial environments.
Quantum steering ellipsoids (QSEs) provide a geometric representation, within the Bloch picture, of all possible states to which one qubit can be steered through measuring another correlated qubit. However, in realistic settings, quantum systems are inevitably coupled to their environment, resulting in decoherence and degradation of the QSE. Here, by investigating how local dissipative environments coupled to each qubit affect the quantum steering, we find that the geometry of each party's QSE is closely tied to the non-Markovian effect and the formation of a bound state in the energy spectrum of the total qubit-environment system. The bound state provides the ability and the non-Markovian effect provides the dynamical way for preserving the QSE. We systematically examine the characteristics of QSEs under three distinct scenarios, i.e., two-sided bound states, one-sided bound states, and no bound state, revealing a diverse range of steering types. Our work establishes quantum reservoir engineering as a tunable strategy for protecting and controlling quantum steering in open systems, offering a practical pathway toward robust steering-based quantum technologies.
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 analyzed in terms of three geometric features of the ellipsoid and prove that a state is separable if and only if it obeys a "nested tetrahedron" condition.
Abstract We investigate tripartite quantum steering dynamics in a three-Unruh–DeWitt-detector system, examining both 1→2 1 → 2 (i.e., from Alice to Bob and Charlie) and 2→1 2 → 1 steering (i.e., from Alice and Bob to Charlie) configurations under two paradigmatic entangled initial states: the Greenberger–Horne–Zeilinger (GHZ) and W states. Our analysis demonstrates that 1→2 1 → 2 steering exhibits better resistance to Unruh decoherence than 2→1 2 → 1 steering. Notably, the 1→2 1 → 2 steering of the W state displays a non-monotonic dependence on the acceleration parameter, indicating that the Unruh effect can, in certain regimes, enhance quantum steering. These results suggest that the Unruh effect plays a dual role in tripartite quantum systems, as it can both enhance and degrade quantum steering. Consequently, moving beyond the conventional interpretation of the Unruh effect as merely a source of decoherence, our study provides a new insight by exploring tripartite quantum steering in a relativistic setting.