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 employed the instantaneous nonlocal effects caused by the collapse of the wavefunction of a single particle-the spooky action at a distance-, when a measurement is done. This historical event preceded the well-know Einstein-Podolsk-Rosen criticism over the incompleteness of quantum mechanics. Here, by using the Stern-Gerlach experiment, we demonstrate how the instantaneous nonlocal feature of the collapse of the wavefunction together with the single-particle entanglement can be used to produce the nonlocal effect of steering, i.e. the single-particle steering. In the steering process Bob gets a quantum state depending on which observable Alice decides to measure. To accomplish this, we fully exploit the spreading (over large distances) of the entangled wavefunction of the single-particle. In particular, we demonstrate that the nonlocality of the single-particle entangled state allows the particle to "know" about the kind of detector Alice is using to steer Bob's state. Therefore, notwithstanding strong counterarguments, we prove that the single-particle entanglement gives rise to truly nonlocal effects at two faraway places. This opens the possibility of using the single-particle entanglement for implementing truly nonlocal task.
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 employed the instantaneous nonlocal effects caused by the collapse of the wavefunction of a single particle-the spooky action at a distance-, when a measurement is done. This historical event preceded the well-know Einstein-Podolsk-Rosen criticism over the incompleteness of quantum mechanics. Here, by using the Stern-Gerlach experiment, we demonstrate how the instantaneous nonlocal feature of the collapse of the wavefunction together with the single-particle entanglement can be used to produce the nonlocal effect of steering, i.e. the single-particle steering. In the steering process Bob gets a quantum state depending on which observable Alice decides to measure. To accomplish this, we fully exploit the spreading (over large distances) of the entangled wavefunction of the single-particle. In particular, we demonstrate that the nonlocality of the single-particle entangled state allows the particle to "know" about the kind of detector Alice is using to steer Bob's state. Therefore, notwithstanding strong counterarguments, we prove that the single-particle entanglement gives rise to truly nonlocal effects at two faraway places. This opens the possibility of using the single-particle entanglement for implementing truly nonlocal task.
Quantum nonlocality and quantum steering are fundamental correlations of quantum systems which cannot 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 where Alice remotely steers Bob's state. Research in nonlocality and steering is of 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, development, and teaching of quantum mechanics and quantum information. In particular, the thought experiment of consecutive Stern-Gerlach experiments is commonly used to exemplify the concept of noncommutativity between quantum operators. However, to the best of our knowledge, the consecutive Stern-Gerlach experiments have not been treated in a fully fledged quantum manner yet, and it is a widely accepted idea that atoms crossing consecutive Stern-Gerlach experiments follow classical paths. Here we demonstrate that two consecutive Stern-Gerlach experiments generate nonlocality and steering, and these nonlocal effects strongly modify our usual understanding of this experiment. Also, we discuss the implications of this result and its relation with entanglement. This suggests the use of quantum correlations, of particles possessing mass, to generate nonlocal tasks using this experiment.
In a recent work [Phys. Rev. Lett. 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 demonstrates the nonlocal effect first identified in the famous Einstein-Podolsky-Rosen paper [Phys. Rev. 47, 777 (1935)] as a universal effect for pure entangled states. This ability of Alice to remotely prepare Bob's state was subsequently called steering by Schr\"odinger, whose terminology we adopt. The phenomenon of steering has been largely overlooked, and prior to our work had not even been given a rigorous definition that is applicable to mixed states as well as pure states. Armed with our rigorous definition, we proved that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. In this work we expand on these results and provide further examples of steerable states. We also elaborate on the connection with the original EPR paradox.
A single quantum particle can be described by a wavefunction that spreads over arbitrarily large distances; however, it is never detected in two (or more) places. This strange phenomenon is explained in the quantum theory by what Einstein repudiated as ‘spooky action at a distance’: the instantaneous nonlocal collapse of the wavefunction to wherever the particle is detected. Here we demonstrate this single-particle spooky action, with no efficiency loophole, by splitting a single photon between two laboratories and experimentally testing whether the choice of measurement in one laboratory really causes a change in the local quantum state in the other laboratory. To this end, we use homodyne measurements with six different measurement settings and quantitatively verify Einstein’s spooky action by violating an Einstein–Podolsky–Rosen-steering inequality by 0.042±0.006. Our experiment also verifies the entanglement of the split single photon even when one side is untrusted. Quantum mechanics exhibit many unusual features, including Einstein’s so-called ‘spooky action at a distance’, wherein a wavefunction collapses at all points except where it is detected. Using homodyne measurements, Fuwa et al. verify this effect for a single photon split between two labs.
According to Schrödinger, the laws of quantum mechanics obliges us to admit that by suitable measurement taken on one of the two system only1 the state of the other system can not only be determined but steered too. That is, it conveys the potential ability to steer the state of another physical system without interacting with it by implementing independent measurements, this nonlocal phenomenon was named steering. On the other hand, the first proposals about the nonlocality of a single photon focus on showing the Bell nonlocality by using a single photon path entanglement. This path entanglement of a single photon was also used for analyzing and experimentally produce the steering of a single photon. However, these established facts have been recently called into question suggesting that single-photon entanglement is not non-local. In this letter, we show that by incorporating and manipulating the internal degrees of freedom of the photon, together with the external path, it is easy to demonstrate the nonlocal effect of steering of a single photon's state. In this sense, the experimental set-up that we propose differs from the one reported in the quantum optics literature which only uses, to the best of our knowledge, the path entanglement of photons for showing the steering phenomenon, i.e. here we exploit the entanglement between the internal and external degrees of freedom of the photon to show this nonlocal effect. The introduction of the photon's internal degrees of freedom in the experimental set-up gives us new insight, advantages and possibilities to control the nonlocal character of the single-photon entangled state.
Schrödinger held that a local quantum system has some objectively real quantum state and no other (hidden) properties. He therefore took the Einstein-Podolsky-Rosen (EPR) phenomenon, which he generalized and called `steering', to require nonlocal wavefunction collapse. Because this would entail faster-than-light (FTL) information transmission, he doubted that it would be seen experimentally. Here we report a demonstration of EPR steering with entangled photon pairs that puts--in Schrödinger's interpretation--a non-zero lower bound on the amount of FTL information transmission. We develop a family of n-setting loss-tolerant EPR-steering inequalities allowing for a size-d classical message sent from Alice's laboratory to Bob's. For the case n=3 and d=2 (one bit) we observe a statistically significant violation. Our experiment closes the efficiency and locality loopholes, and we address the freedom-of-choice loophole by using quantum random number generators to independently choose Alice's and Bob's measurement basis settings. To close the efficiency and locality loopholes simultaneously, we introduce methods for quickly switching between three mutually unbiased measurement bases and for accurately characterizing the efficiency of detectors. From the space-time arrangement of our experiment, we can conclude that if the mechanism for the observed bipartite correlations is that Alice's measurement induces wave-function collapse of Bob's particle, then more than one bit of information must travel from Alice to Bob at more than three times the speed of light.
Einstein-Podolsky-Rosen steering is a form of quantum nonlocality exhibiting an inherent asymmetry between the observers, Alice and Bob. A natural question is then whether there exist entangled states which are one-way steerable, that is, Alice can steer Bob's state, but it is impossible for Bob to steer the state of Alice. So far, such a phenomenon has been demonstrated for continuous variable systems, but with a strong restriction on allowed measurements, namely, considering only Gaussian measurements. Here we present a simple class of entangled two-qubit states which are one-way steerable, considering arbitrary projective measurements. This shows that the nonlocal properties of entangled states can be fundamentally asymmetrical.