Marek Żukowski

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 non-locality—it ainʼt necessarily so...

Bellʼs theorem is 50 years old. There still remains a controversy about its implications. Much of this controversy has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bellʼs inequalities requires just a locality assumption and nothing more. Violations of the inequalities are then interpreted as a non-locality or quantum non-locality. We show that such claims are unfounded and that every derivation of Bellʼs inequalities requires a premise—in addition to locality and freedom of choice—which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (such as Bellʼs local causality). The premise is equivalent to the assumption of the existence of additional variables which do not appear in the quantum formalism (in the form of determinism, joint probability for outcomes of all conceivable measurements, additional causes, hidden variables, complete description of the state or counterfactual definiteness, etc). A certain irony is that perhaps the main message of the violation of Bellʼs inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 50 years of Bells theorem.

Comment on: Nonlocal “Realistic” Leggett Models Can be Considered Refuted by the Before-Before Experiment

It is shown here that Suarez (Found. Phys. 38:583, 2008) wrongly presents the assumptions behind the Leggett’s inequalities, and their modified form used by Groeblacher et al. (Nature 446:871, 2007) for an experimental falsification of a certain class of non-local hidden variable models.

Generalized quantum measurements and local realism

Following the ideas of Popescu, the generic structure of any local hidden variable model for experiments involving sequences of measurements is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are explicitly derived. The violation of local realism in the case of ``hidden nonlocality is illustrated by an operational example.

Space QUEST mission proposal: experimentally testing decoherence due to gravity

Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum correlations, such as entanglement, may exhibit different behavior to purely classical correlations in curved space. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph et al [5] and Ralph and Pienaar [1], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agencys Space QUEST (Space-Quantum Entanglement Space Test) mission, and study the feasibility of the mission scheme.

Solving large-scale optimization problems related to Bell's Theorem

Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth description of a method of testing the existence of such models, which involves two levels of optimization: a higher-level non-linear task and a lower-level linear programming (LP) task. The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with an innovative matrix-free interior point method. We describe in detail how the latter can be applied to our problem, discuss the basic scenario and possible improvements and how they impact on overall performance. Significant performance advantage of the matrix-free interior point method over the simplex method is confirmed by extensive computational results. The new method is able to solve substantially larger problems. Consequently, the noise resistance of the non-classicality of correlations of several types of quantum states, which has never been computed before, can now be efficiently determined. An extensive set of data in the form of tables and graphics is presented and discussed. The article is intended for all audiences, no quantum-mechanical background is necessary.

Unexpected reemergence of the von Neumann theorem

Is is shown here that the simple test of quantumness for a single system of arXiv:0704.1962 (for a recent experimental realization see arXiv:0804.1646) has exactly the same relation to the discussion of to the problem of describing the quantum system via a classical probabilistic scheme (that is in terms of hidden variables, or within a realistic theory) as the von Neumann theorem (1932). The latter one was shown by Bell (1966) to stem from an assumption that the hidden variable values for a sum of two non-commuting observables (which is an observable too) have to be, for each individual system, equal to sums of eigenvalues of the two operators. One cannot find a physical justification for such an assumption to hold for non-commeasurable variables. On the positive side. the criterion may be useful in rejecting models which are based on stochastic classical fields. Nevertheless the example used by the Authors has a classical optical realization.

Detecting genuine multipartite entanglement of pure states with bipartite correlations

Monogamy of bipartite correlations leads, for arbitrary pure multiqubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable of excluding the possibility of

Bell's theorem tells us NOT what quantum mechanics IS, but what quantum mechanics IS NOT

k

Entanglement criteria for noise resistance of two-qudit states

separability.