Dagomir Kaszlikowski

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.

Minimal qubit tomography

We present, and analyze thoroughly, a highly symmetric and efficient scheme for the determination of a single-qubit state, such as the polarization properties of photons emitted by a single-photon source. In our scheme there are only four measured probabilities, just enough for the determination of the three parameters that specify the qubit state, whereas the standard procedure would measure six probabilities.

Security of quantum key distributions with entangled qudits

We consider a generalization of Ekerts entanglement-based quantum cryptographic protocol where qubits are replaced by N- or d-dimensional systems (qudits). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerfs formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of qudit generalizations of the Ekerts protocol for qubits.

Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states

The N-qubit states of the W class, for N>10, lead to more robust (against noise admixture) violations of local realism, than the GHZ states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining (N-2) qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.

Entropic test of quantum contextuality.

We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an entropic contextual inequality is formulated, analogous to the entropic Bell inequalities derived by Braunstein and Caves [Phys. Rev. Lett. 61, 662 (1988)], that must be satisfied by all noncontextual theories. We find optimal measurements for violation of this inequality. The approach is easily extendable to higher dimensional quantum systems and more measurements. Our theoretical findings can be verified in the laboratory with current technology.

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.

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 birds 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.

WAVE-PARTICLE DUALITY IN MULTI-PATH INTERFEROMETERS: GENERAL CONCEPTS AND THREE-PATH INTERFEROMETERS

For two-path interferometers, the which-path predictability and the fringe visibility are familiar quantities that are much used to talk about wave-particle duality in a quantitative way. We discuss several candidates that suggest themselves as generalizations P of for multi-path interferometers, and treat the case of three paths in considerable detail. To each choice for the path knowledge P, the interference strength V — the corresponding generalization of — is found by a natural, operational procedure. In experimental terms, it amounts to finding those equal-weight superpositions of the path amplitudes which maximize P for the emerging intensities. Mathematically speaking, one needs to identify a certain optimum one among the Fourier transforms of the state of the interfering quantum object. Wave-particle duality is manifest, inasmuch as P = 1 implies V = 0 and V = 1 implies P = 0, whatever definition is chosen. The possible values of the pair (P,V) are restricted to an area with corners at (P,V) = (0,0), (P,V) = (1,0), and (P,V) = (0,1), with the shape of the border line from (1,0) to (0,1), depending on the particular choice for P and the induced definition of V.

Entangled three-state systems violate local realism more strongly than qubits: An analytical proof

In Kaszlikowski [Phys. Rev. Lett. {\bf 85}, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled