In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.
In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.
The Greenberger-Horne-Zeilinger (GHZ) version of the Einstein-Podolsky-Rosen (EPR) paradox is widely regarded as a conclusive logical argument that rules out the possibility of describing quantum phenomena within the framework of any model of local hidden variables in which the observers are free to choose their own experimental settings. In this paper, we show, however, that the GHZ argument implicitly relies on a subtle, though crucial, assumption that is not required by fundamental physical principles, and which had gone unnoticed. Namely, we note that the argument implicitly assumes the existence of an absolute angular frame of reference with respect to which the polarization properties of the hypothetical hidden configurations of the entangled particles, as well as the orientations of the measurement devices that test them, can be defined. We further note that such an absolute frame of reference may not exist if the hidden configurations of the entangled particles spontaneously break the gauge rotational symmetry. Indeed, by skipping the disputed requirement we are able to build a model of local hidden variables for the GHZ state, which complies with the 'free-will' hypothesis and reproduces the quantum mechanical predictions. Our model, thus, completes-in the EPR sense-the quantum description of the GHZ state.
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 amenable to an experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is more friendly for experimental implementation, i.e., one may only measure the observables in x-, y-, or z-axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with the theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.
Einstein–Podolsky–Rosen (EPR) paradox highlights the absence of a local realistic explanation for quantum mechanics, and shows the incompatibility of the local-hidden-state models with quantum theory. For N-qubit states, or more importantly, the N-qubit mixed states, we present the EPR steering paradox in the form of the contradictory equality “[Formula: see text]”. We show that the contradiction holds for any N-qubit state as long as both “the pure state requirement” and “the measurement requirement” are satisfied. This also indicates that the EPR steering paradox exists in more general cases. Finally, we give specific examples to demonstrate and analyze our arguments.
The Einstein–Podolsky–Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of a local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of “quantum nonlocality,” which manifests itself in three types: quantum entanglement, quantum steering, and Bell’s nonlocality. Although Bell’s nonlocality is more often used to show “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 amenable to experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is friendlier for experimental implementation, i.e., one may measure the observables only in the x , y , or z axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.
The Einstein-Podolsky-Rosen (EPR) paradox is one of the earliest paradoxes, arising from the lack of local realistic description of mechanics. The EPR paradox leads to the important concept of quantum which manifests itself by three different phenomena: entanglement, steering, and Bell's nonlocality. Two well-known paradoxes related to Bell's nonlocality, i.e. the Greenberger-Horne-Zeilinger paradox and the Hardy paradox, have been widely studied and also experimentally confirmed. However, an experimental test of the EPR paradox is still lacking. The EPR paradox is essentially a steering paradox, and recently it has been mathematically formulated as a contradiction equality k=1, thus making it amenable to an experimental verification. Moreover, based on the EPR paradox we also derive a generalized linear steering inequality. In this work, we perform the first experimental test of the EPR paradox in a two-qubit scenario, and also verify the corresponding generalized steering inequality, which has an advantage over the usual one by detecting more steerability of states. Experimental results confirm the theoretical predictions within the experimental errors, and provide a deeper understanding of foundation.
Abstract Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocality between entanglement and Bell’s nonlocality emphasizing the incompatibility of the local-hidden-state (LHS) model with quantum theory. It is well established that the EPR steering paradox is an essential method for determining steering, which reveals the nature of steering by logical contradiction. However, previous studies on the EPR steering paradox have only examined cases where the conditional states of the steered party are pure. In this work, we present the EPR steering paradox about the case when the conditional states of the steered party are mixed, which can be expressed as a paradoxical equality ‘ 2 Q = 2 − δ C ’ 0 < δ < 1 given by quantum (Q) and classical (C) theories. For any N-qubit state, in the two-setting steering protocol, the contradiction ‘ 2 Q = 2 − δ C ’ can be obtained if and only if a particular set of projective measurements of the steering party makes all the conditional states of the steered party pure, which also implies that the N-qubit state is steerable. Moreover, considering the conditional states of the steered party as mixed states, we are able to identify the full range of steerable states detectable through the EPR steering paradox method. This also means that, so far, one has found all the steerable states that can be recognized by the EPR steering paradox, which is significant for some typical quantum schemes such as quantum teleportation and quantum key distribution.