### Concept: Bell's theorem

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##### Conclusive quantum steering with superconducting transition-edge sensors.

- OPEN
- Nature communications
- Published over 6 years ago
- Discuss

Quantum steering allows two parties to verify shared entanglement even if one measurement device is untrusted. A conclusive demonstration of steering through the violation of a steering inequality is of considerable fundamental interest and opens up applications in quantum communication. To date, all experimental tests with single-photon states have relied on post selection, allowing untrusted devices to cheat by hiding unfavourable events in losses. Here we close this ‘detection loophole’ by combining a highly efficient source of entangled photon pairs with superconducting transition-edge sensors. We achieve an unprecedented ∼62% conditional detection efficiency of entangled photons and violate a steering inequality with the minimal number of measurement settings by 48 s.d.s. Our results provide a clear path to practical applications of steering and to a photonic loophole-free Bell test.

#### 51

##### Satellite-based entanglement distribution over 1200 kilometers

- Science (New York, N.Y.)
- Published 10 months ago
- Discuss

Long-distance entanglement distribution is essential for both foundational tests of quantum physics and scalable quantum networks. Owing to channel loss, however, the previously achieved distance was limited to ~100 kilometers. Here we demonstrate satellite-based distribution of entangled photon pairs to two locations separated by 1203 kilometers on Earth, through two satellite-to-ground downlinks with a summed length varying from 1600 to 2400 kilometers. We observed a survival of two-photon entanglement and a violation of Bell inequality by 2.37 ± 0.09 under strict Einstein locality conditions. The obtained effective link efficiency is orders of magnitude higher than that of the direct bidirectional transmission of the two photons through telecommunication fibers.

#### 32

##### Connection between Bell nonlocality and Bayesian game theory

- Nature communications
- Published almost 5 years ago
- Discuss

In 1964, Bell discovered that quantum mechanics is a nonlocal theory. Three years later, in a seemingly unconnected development, Harsanyi introduced the concept of Bayesian games. Here we show that, in fact, there is a deep connection between Bell nonlocality and Bayesian games, and that the same concepts appear in both fields. This link offers interesting possibilities for Bayesian games, namely of allowing the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signalling boxes. This will lead to novel joint strategies, impossible to achieve classically. We characterize games for which nonlocal resources offer a genuine advantage over classical ones. Moreover, some of these strategies represent equilibrium points, leading to the notion of quantum/no-signalling Nash equilibrium. Finally, we describe new types of question in the study of nonlocality, namely the consideration of nonlocal advantage given a set of Bell expressions.

#### 20

##### High-dimensional entanglement certification

- OPEN
- Scientific reports
- Published almost 2 years ago
- Discuss

Quantum entanglement is the ability of joint quantum systems to possess global properties (correlation among systems) even when subsystems have no definite individual property. Whilst the 2-dimensional (qubit) case is well-understood, currently, tools to characterise entanglement in high dimensions are limited. We experimentally demonstrate a new procedure for entanglement certification that is suitable for large systems, based entirely on information-theoretics. It scales more efficiently than Bell’s inequality and entanglement witness. The method we developed works for arbitrarily large system dimension d and employs only two local measurements of complementary properties. This procedure can also certify whether the system is maximally entangled. We illustrate the protocol for families of bipartite states of qudits with dimension up to 32 composed of polarisation-entangled photon pairs.

#### 16

##### Experimental test of nonlocal causality

- OPEN
- Science advances
- Published over 1 year ago
- Discuss

Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell’s local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect.

#### 10

From dice to modern electronic circuits, there have been many attempts to build better devices to generate random numbers. Randomness is fundamental to security and cryptographic systems and to safeguarding privacy. A key challenge with random-number generators is that it is hard to ensure that their outputs are unpredictable1-3. For a random-number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model that describes the underlying physics is necessary to assert unpredictability. Imperfections in the model compromise the integrity of the device. However, it is possible to exploit the phenomenon of quantum non-locality with a loophole-free Bell test to build a random-number generator that can produce output that is unpredictable to any adversary that is limited only by general physical principles, such as special relativity1-11. With recent technological developments, it is now possible to carry out such a loophole-free Bell test12-14,22. Here we present certified randomness obtained from a photonic Bell experiment and extract 1,024 random bits that are uniformly distributed to within 10-12. These random bits could not have been predicted according to any physical theory that prohibits faster-than-light (superluminal) signalling and that allows independent measurement choices. To certify and quantify the randomness, we describe a protocol that is optimized for devices that are characterized by a low per-trial violation of Bell inequalities. Future random-number generators based on loophole-free Bell tests may have a role in increasing the security and trust of our cryptographic systems and infrastructure.

#### 10

##### Practical device-independent quantum cryptography via entropy accumulation

- OPEN
- Nature communications
- Published 3 months ago
- Discuss

Device-independent cryptography goes beyond conventional quantum cryptography by providing security that holds independently of the quality of the underlying physical devices. Device-independent protocols are based on the quantum phenomena of non-locality and the violation of Bell inequalities. This high level of security could so far only be established under conditions which are not achievable experimentally. Here we present a property of entropy, termed “entropy accumulation”, which asserts that the total amount of entropy of a large system is the sum of its parts. We use this property to prove the security of cryptographic protocols, including device-independent quantum key distribution, while achieving essentially optimal parameters. Recent experimental progress, which enabled loophole-free Bell tests, suggests that the achieved parameters are technologically accessible. Our work hence provides the theoretical groundwork for experimental demonstrations of device-independent cryptography.

#### 8

##### Bell correlations in a Bose-Einstein condensate

- Science (New York, N.Y.)
- Published about 2 years ago
- Discuss

Characterizing many-body systems through the quantum correlations between their constituent particles is a major goal of quantum physics. Although entanglement is routinely observed in many systems, we report here the detection of stronger correlations–Bell correlations–between the spins of about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation witness from a many-particle Bell inequality involving only one- and two-body correlation functions. Our measurement on a spin-squeezed state exceeds the threshold for Bell correlations by 3.8 standard deviations. Our work shows that the strongest possible nonclassical correlations are experimentally accessible in many-body systems and that they can be revealed by collective measurements.

#### 7

Precision control over hybrid physical systems at the quantum level is important for the realization of many quantum-based technologies. In the field of quantum information processing (QIP) and quantum networking, various proposals discuss the possibility of hybrid architectures where specific tasks are delegated to the most suitable subsystem. For example, in quantum networks, it may be advantageous to transfer information from a subsystem that has good memory properties to another subsystem that is more efficient at transporting information between nodes in the network. For trapped ions, a hybrid system formed of different species introduces extra degrees of freedom that can be exploited to expand and refine the control of the system. Ions of different elements have previously been used in QIP experiments for sympathetic cooling, creation of entanglement through dissipation, and quantum non-demolition measurement of one species with another. Here we demonstrate an entangling quantum gate between ions of different elements which can serve as an important building block of QIP, quantum networking, precision spectroscopy, metrology, and quantum simulation. A geometric phase gate between a (9)Be(+) ion and a (25)Mg(+) ion is realized through an effective spin-spin interaction generated by state-dependent forces induced with laser beams. Combined with single-qubit gates and same-species entangling gates, this mixed-element entangling gate provides a complete set of gates over such a hybrid system for universal QIP. Using a sequence of such gates, we demonstrate a CNOT (controlled-NOT) gate and a SWAP gate. We further demonstrate the robustness of these gates against thermal excitation and show improved detection in quantum logic spectroscopy. We also observe a strong violation of a CHSH (Clauser-Horne-Shimony-Holt)-type Bell inequality on entangled states composed of different ion species.

#### 7

##### Bell’s inequality violation with spins in silicon

- Nature nanotechnology
- Published over 2 years ago
- Discuss

Bell’s theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell’s inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity.