Monogamy of Particle Statistics in Tripartite Systems Simulating Bosons and Fermions.

In the quantum world, correlations can take the form of entanglement which is known to be monogamous. In this Letter we show that another type of correlation, indistinguishability, is also restricted by some form of monogamy. Namely, if particles A and B simulate bosons, then A and C cannot perfectly imitate fermions. Our main result consists in demonstrating to what extent it is possible.

Generalized Probabilistic Description of Noninteracting Identical Particles.

We investigate an operational description of identical noninteracting particles in multiports. In particular, we look for physically motivated restrictions that explain their bunching probabilities. We focus on a symmetric 3-port in which a triple of superquantum particles admitted by our generalized probabilistic framework would bunch with a probability of 3/4. The bosonic bound of 2/3 can then be restored by imposing the additional requirement of product evolution of certain input states. These states are characterized by the fact that, much like product states, their entropy equals the sum of entropies of their one-particle substates. This principle is, however, not enough to exclude the possibility of superquantum particles in higher-order multiports.

Experimental Detection of Information Deficit in a Photonic Contextuality Scenario.

Contextuality is an essential characteristic of quantum theory, and supplies the power for many quantum information processes. Previous tests of contextuality focus mainly on the probability distribution of measurement results. However, a test of contextuality can be formulated in terms of entropic inequalities whose violations imply information deficit in the studied system. This information deficit has not been observed on a single local system. Here we report the first experimental detection of information deficit in an entropic test of quantum contextuality based on photonic setup. The corresponding inequality is violated with more than 13 standard deviations.

Entropic Tests of Multipartite Nonlocality and State-Independent Contextuality.

We introduce a multipartite extension of an information-theoretic distance introduced by Zurek [Nature (London) 341, 119 (1989)]. We use it to develop a new tool for studying quantum correlations from an information-theoretic perspective. In particular, we derive entropic tests of multipartite nonlocality for three qubits and for an arbitrary even number of qubits as well as a test of state-independent contextuality. In addition, we rederive the tripartite Mermin inequality and a state-independent noncontextuality inequality by Cabello [Phys. Rev. Lett. 101, 210401 (2008)]. This suggests that the information-theoretic distance approach to multipartite nonlocality and state-independent contextuality can provide a more general treatment of nonclassical correlations than the orthodox approach based on correlation functions.

Fundamental monogamy relation between contextuality and nonlocality.

We show that the no-disturbance principle imposes a tradeoff between locally contextual correlations violating the Klyachko-Can-Biniciogˇlu-Shumovski inequality and spatially separated correlations violating the Clauser-Horne-Shimony-Holt inequality. The violation of one inequality forbids the violation of the other. We also obtain the corresponding monogamy relation imposed by quantum theory for a qutrit-qubit system. Our results show the existence of fundamental monogamy relations between contextuality and nonlocality that suggest that entanglement might be a particular form of a more fundamental resource.

Contextuality in bosonic bunching.

In the classical probability theory a sum of probabilities of three pairwise exclusive events is always bounded by one. This is also true in quantum mechanics if these events are represented by pairwise orthogonal projectors. However, this might not be true if the three events refer to a system of indistinguishable particles. We show that one can find three pairwise exclusive events for a system of three bosonic particles whose corresponding probabilities sum to 3/2. This can be done under assumptions of realism and noncontextuality, i.e., that it is possible to assign outcomes to events before measurements are performed and in a way that does not depend on a particular measurement setup. The root of this phenomenon comes from the fact that for indistinguishable particles there are events that can be deduced to be exclusive under the aforementioned assumptions, but at the same time are complementary because the corresponding projectors are not orthogonal.

An experimental proposal for revealing contextuality in almost all qutrit states.

Contextuality is a foundational phenomenon underlying key differences between quantum theory and classical realistic descriptions of the world. Here we propose an experimental test which is capable of revealing contextuality in all qutrit systems, except the completely mixed state, provided we choose the measurement basis appropriately. The 3-level system is furnished by the polarization and spatial degrees of freedom of a single photon, which encompass three orthogonal modes. Projective measurements along rays in the 3-dimensional Hilbert space are made by linear optical elements and detectors which are sensitive to single mode. We also discuss the impact of detector inefficiency and losses and review the theoretical foundations of this test.

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.

Generalized monogamy of contextual inequalities from the no-disturbance principle.

In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs admit a joint probability distribution, we formulate a precise graph-theoretic condition that gives rise to the monogamy of contextuality. We also show how such monogamies arise within quantum theory for a single four-dimensional system and interpret violation of these relations in terms of a violation of causality. These monogamies can be tested with current experimental techniques.

Optimal cloning and singlet monogamy.

The inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins. Despite this, there is no quantitative link between how much entanglement can be generated between spins, and how well an unknown state can be cloned. This situation is remedied by giving a set of sufficient conditions such that a Completely Positive map can be optimally implemented as a teleportation operation into a standard, reference, state. The case of arbitrary 1-->N asymmetric cloning of d-dimensional spins can then be solved exactly, yielding the concept of "singlet monogamy." The utility of this relation is demonstrated by calculating properties of Heisenberg systems, and contrasting them with the results from standard monogamy arguments.

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.

Quantum correlation without classical correlations.

We show that genuine multiparty quantum correlations can exist on its own, without a supporting background of genuine multiparty classical correlations, even in macroscopic systems. Such possibilities can have important implications in the physics of quantum information and phase transitions.

Regional versus global entanglement in resonating-valence-bond states.

We investigate the entanglement properties of resonating-valence-bond states on two and higher dimensional lattices, which play a significant role in our understanding of various many-body systems. We show that these states are genuinely multipartite entangled, while there is only a negligible amount of two-site entanglement. We comment on possible physical implications of our findings.

Tomographic quantum cryptography: equivalence of quantum and classical key distillation.

The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.

Information-theoretic approach to single-particle and two-particle interference in multipath interferometers.

We propose entropic measures for the strength of single-particle and two-particle interference in interferometric experiments where each particle of a pair traverses a multipath interferometer. Optimal single-particle interference excludes any two-particle interference, and vice versa. We report an inequality that states the compromises allowed by quantum mechanics in intermediate situations, and identify a class of two-particle states for which the upper bound is reached. Our approach is applicable to symmetric two-partite systems of any finite dimension.