Numerical tests of magnetoreception models assisted with behavioral experiments on American cockroaches.

Many animals display sensitivity to external magnetic field, but it is only in the simplest organisms that the sensing mechanism is understood. Here we report on behavioural experiments where American cockroaches (Periplaneta americana) were subjected to periodically rotated external magnetic fields with a period of 10 min. The insects show increased activity when placed in a periodically rotated Earth-strength field, whereas this effect is diminished in a twelve times stronger periodically rotated field. We analyse established models of magnetoreception, the magnetite model and the radical pair model, in light of this adaptation result. A broad class of magnetite models, based on single-domain particles found in insects and assumption that better alignment of magnetic grains towards the external field yields better sensing and higher insect activity, is shown to be excluded by the measured data. The radical-pair model explains the data if we assume that contrast in the chemical yield on the order of one in a thousand is perceivable by the animal, and that there also exists a threshold value for detection, attained in an Earth-strength field but not in the stronger field.

Creating and concentrating quantum resource states in noisy environments using a quantum neural network.

Quantum information processing tasks require exotic quantum states as a prerequisite. They are usually prepared with many different methods tailored to the specific resource state. Here we provide a versatile unified state preparation scheme based on a driven quantum network composed of randomly-coupled fermionic nodes. The output of such a system is then superposed with the help of linear mixing where weights and phases are trained in order to obtain desired output quantum states. We explicitly show that our method is robust and can be utilized to create almost perfect maximally entangled, NOON, W, cluster, and discorded states. Furthermore, the treatment includes energy decay in the system as well as dephasing and depolarization. Under these noisy conditions we show that the target states are achieved with high fidelity by tuning controllable parameters and providing sufficient strength to the driving of the quantum network. Finally, in very noisy systems, where noise is comparable to the driving strength, we show how to concentrate entanglement by mixing more states in a larger network.

Reconstructing Quantum States With Quantum Reservoir Networks.

Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary quantum states is challenging as the paradigm of efficient protocols has remained in applying specific techniques for different types of quantum states. Here, we introduce a quantum state tomography platform based on the framework of reservoir computing. It forms a quantum neural network and operates as a comprehensive device for reconstructing an arbitrary quantum state (finite-dimensional or continuous variable). This is achieved with only measuring the average occupation numbers in a single physical setup, without the need of any knowledge of optimum measurement basis or correlation measurements.

Quantum Neuromorphic Platform for Quantum State Preparation.

We develop a scheme of quantum reservoir state preparation, based on a quantum neural network framework, which takes classical optical excitation as input and provides desired quantum states as output. We theoretically demonstrate the broad potential of our scheme by explicitly preparing a range of intriguing quantum states, including single-photon states, Schrödinger's cat states, and two-mode entangled states. This scheme can be used as a compact quantum state preparation device for emerging quantum technologies.

In-vivo biomagnetic characterisation of the American cockroach.

We present a quantitative method, utilising a highly sensitive quantum sensor, that extends applicability of magnetorelaxometry to biological samples at physiological temperature. The observed magnetic fields allow for non-invasive determination of physical properties of magnetic materials and their surrounding environment inside the specimen. The method is applied to American cockroaches and reveals magnetic deposits with strikingly different behaviour in alive and dead insects. We discuss consequences of this finding to cockroach magneto-reception. To our knowledge, this work represents the first characterisation of the magnetisation dynamics in live insects and helps to connect results from behavioural experiments on insects in magnetic fields with characterisation of magnetic materials in their corpses.

Revealing Nonclassicality of Inaccessible Objects.

Some physical objects are hardly accessible to direct experimentation. It is then desirable to infer their properties based solely on the interactions they have with systems over which we have control. In this spirit, here we introduce schemes for assessing the nonclassicality of the inaccessible objects as characterized by quantum discord. We consider two probes individually interacting with the inaccessible object but not with each other. The schemes are based on monitoring entanglement dynamics between the probes. Our method is robust and experimentally friendly, as it allows the probes and the object to be open systems and makes no assumptions about the initial state, dimensionality of involved Hilbert spaces, and details of the probe-object Hamiltonian. We apply our scheme to a membrane-in-the-middle optomechanical system, to detect system-environment correlations in open system dynamics as well as nonclassicality of the environment, and we foresee potential benefits for the inference of the nonclassical nature of gravity.

Nonclassicality of Temporal Correlations.

The results of spacelike separated measurements are independent of distant measurement settings, a property one might call two-way no-signaling. In contrast, timelike separated measurements are only one-way no-signaling since the past is independent of the future but not vice versa. For this reason some temporal correlations that are formally identical to nonclassical spatial correlations can still be modeled classically. We propose a new formulation of Bell's theorem for temporal correlations; namely, we define nonclassical temporal correlations as the ones which cannot be simulated by propagating in time the classical information content of a quantum system given by the Holevo bound. We first show that temporal correlations between results of any projective quantum measurements on a qubit can be simulated classically. Then we present a sequence of general measurements on a single m-level quantum system that cannot be explained by propagating in time an m-level classical system and using classical computers with unlimited memory.

Genuine Multipartite Entanglement without Multipartite Correlations.

Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.

Bandyopadhyay, Paterek, and Kaszlikowski reply.

In this Reply to the preceding Comment by Gauger and Benjamin, we recognize that the numerical error was present in our software, and we explain which of our conclusions are affected by it.

Quantum coherence and sensitivity of avian magnetoreception.

Migratory birds and other species have the ability to navigate by sensing the geomagnetic field. Recent experiments indicate that the essential process in the navigation takes place in the bird's eye and uses chemical reaction involving molecular ions with unpaired electron spins (radical pair). Sensing is achieved via geomagnetic-dependent dynamics of the spins of the unpaired electrons. Here we utilize the results of two behavioral experiments conducted on European robins to argue that the average lifetime of the radical pair is of the order of a microsecond and therefore agrees with experimental estimations of this parameter for cryptochrome--a pigment believed to form the radical pairs. We also find a reasonable parameter regime where the sensitivity of the avian compass is enhanced by environmental noise, showing that long coherence time is not required for navigation and may even spoil it.

Experimental Schmidt decomposition and state independent entanglement detection.

We introduce an experimental procedure for the detection of quantum entanglement of an unknown quantum state with a small number of measurements. The method requires neither a priori knowledge of the state nor a shared reference frame between the observers and can thus be regarded as a perfectly state-independent entanglement witness. The scheme starts with local measurements, possibly supplemented with suitable filtering, which essentially establishes the Schmidt decomposition for pure states. Alternatively we develop a decision tree that reveals entanglement within few steps. These methods are illustrated and verified experimentally for various entangled states of two and three qubits.

Unified view of quantum and classical correlations.

We discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to put all correlations on an equal footing. Entanglement and dissonance, whose definition is introduced here, jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states.

Information causality as a physical principle.

Quantum physics has remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (non-determinism) and does not allow copying of unknown states (no-cloning). Quantum correlations may be stronger than any classical ones, but information cannot be transmitted faster than light (no-signalling). However, these features do not uniquely define quantum physics. A broad class of theories exist that share such traits and allow even stronger (than quantum) correlations. Here we introduce the principle of 'information causality' and show that it is respected by classical and quantum physics but violated by all no-signalling theories with stronger than (the strongest) quantum correlations. The principle relates to the amount of information that an observer (Bob) can gain about a data set belonging to another observer (Alice), the contents of which are completely unknown to him. Using all his local resources (which may be correlated with her resources) and allowing classical communication from her, the amount of information that Bob can recover is bounded by the information volume (m) of the communication. Namely, if Alice communicates m bits to Bob, the total information obtainable by Bob cannot be greater than m. For m = 0, information causality reduces to the standard no-signalling principle. However, no-signalling theories with maximally strong correlations would allow Bob access to all the data in any m-bit subset of the whole data set held by Alice. If only one bit is sent by Alice (m = 1), this is tantamount to Bob's being able to access the value of any single bit of Alice's data (but not all of them). Information causality may therefore help to distinguish physical theories from non-physical ones. We suggest that information causality-a generalization of the no-signalling condition-might be one of the foundational properties of nature.

Efficient hidden-variable simulation of measurements in quantum experiments.

We prove that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using a polynomial (in measurements) number of hidden-variable states. In the limit of infinitely many measurements, our method gives models with the minimal number of hidden-variable states, which scales linearly with the number of measurements. These results can find applications in foundations of quantum theory, complexity studies, and classical simulations of quantum systems.

Experimentally friendly geometrical criteria for entanglement.

A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.

An experimental test of non-local realism.

Most working scientists hold fast to the concept of 'realism'--a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned.

Experimental test of nonlocal realistic theories without the rotational symmetry assumption.

We analyze the class of nonlocal realistic theories that was originally considered by Leggett [Found. Phys. 33, 1469 (2003)10.1023/A:1026096313729] and tested by us in a recent experiment [Nature (London) 446, 871 (2007)10.1038/nature05677]. We derive an incompatibility theorem that works for finite numbers of polarizer settings and that does not require the previously assumed rotational symmetry of the two-particle correlation functions. The experimentally measured case involves seven different measurement settings. Using polarization-entangled photon pairs, we exclude this broader class of nonlocal realistic models by experimentally violating a new Leggett-type inequality by 80 standard deviations.

Tight multipartite Bell's inequalities involving many measurement settings.

We derive tight Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are violated by some classes of states, for which all standard Bell's inequalities with two measurement settings per observer are satisfied.