Publications, Jan-Åke Larsson, Docent, PhD

Entanglement and its consequences—in particular the violation of Bell inequalities, which defies our concepts of realism and locality—have been proven to play key roles in Nature by many experiments for various quantum systems. Entanglement can also be found in systems not consisting of ordinary matter and light, i.e. in massive meson–antimeson systems. Bell inequalities have been discussed for these systems, but up to date no direct experimental test to conclusively exclude local realism was found. This mainly stems from the fact that one only has access to a restricted class of observables and that these systems are also decaying. In this Letter we put forward a Bell inequality for unstable systems which can be tested at accelerator facilities with current technology. Herewith, the long awaited proof that such systems at different energy scales can reveal the sophisticated “dynamical” nonlocal feature of Nature in a direct experiment gets feasible. Moreover, the role of entanglement and violation, an asymmetry between matter and antimatter, is explored, a special feature offered only by these meson–antimeson systems.

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimum amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information-carrying capacity of the system.

A cell lineage is the ancestral relationship between a group of cells that originate from a single founder cell. For example, in the embryo of the nematode Caenorhabditis elegans an invariant cell lineage has been traced, and with this information at hand it is possible to theoretically model the emergence of different cell types in the lineage, starting from the single fertilized egg. In this report we outline a modelling technique for cell lineage trees, which can be used for the C. elegans embryonic cell lineage but also extended to other lineages. The model takes into account both cell-intrinsic (transcription factor-based) and -extrinsic (extracellular) factors as well as synergies within and between these two types of factors. The model can faithfully recapitulate the entire C. elegans cell lineage, but is also general, i.e., it can be applied to describe any cell lineage. We show that synergy between factors, as well as the use of extrinsic factors, drastically reduce the number of regulatory factors needed for recapitulating the lineage. The model gives indications regarding co-variation of factors, number of involved genes and where in the cell lineage tree that asymmetry might be controlled by external influence. Furthermore, the model is able to emulate other (Boolean, discrete and differential-equation-based) models. As an example, we show that the model can be translated to the language of a previous linear sigmoid-limited concentration-based model (Geard and Wiles, 2005). This means that this latter model also can exhibit synergy effects, and also that the cumbersome iterative technique for parameter estimation previously used is no longer needed. In conclusion, the proposed model is general and simple to use, can be mapped onto other models to extend and simplify their use, and can also be used to indicate where synergy and external influence would reduce the complexity of the regulatory process.

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A basic assumption behind the inequalities used for testing noncontextual hidden variable models is that the observables measured on the same individual system are perfectly compatible. However, compatibility is not perfect in actual experiments using sequential measurements. We discuss the resulting "compatibility loophole" and present several methods to rule out certain hidden variable models that obey a kind of extended noncontextuality. Finally, we present a detailed analysis of experimental imperfections in a recent trapped-ion experiment and apply our analysis to that case.

The chained Bell inequalities of Braunstein and Caves involving N settings per observer have some interesting applications. Here we obtain the minimum detection efficiency required for a loophole-free violation of the Braunstein-Caves inequalities for any N greater than= 2. We discuss both the case in which both particles are detected with the same efficiency and the case in which the particles are detected with different efficiencies.

De Raedt et al. [Eur. Phys. J. B 53, 139 (2006)] have claimed to provide a local realist model for correlations of the singlet state in the familiar Einstein-Podolsky-Rosen-Bohm (EPRB) experiment when time-coincidence is used to decide which detection events should count in the analysis, and furthermore that this suggests that it is possible to construct local realistic models that can reproduce the quantum mechanical expectation values. In this letter we show that these conclusions cannot be upheld since their model exploits the so-called coincidence-time loophole. When this is properly taken into account no startling conclusions can be drawn about local realist modelling of quantum mechanics.

The bits of the binary expansion of position measurement results were used to derive Bell inequalities for position measurements. The output state of the nondegenerate optical parametric amplifier (NOPA) was used to obtain violations of these inequalities. It was shown that the position operator itself, together with other suitable operators, also can be used to violate the Bell inequality, deriving a Bell inequality more suited to the original Einstein-Podolsky-Rosen (EPR) setting. It was concluded that the NOPA state cannot be described by a local realist model, despite having a strictly positive Wigner function.

This paper analyzes effects of time dependence in the Bell inequality. A generalized inequality is derived for the case when coincidence and non-coincidence (and hence whether or not a pair contributes to the actual data) is controlled by timing that depends on the detector settings. Needless to say, this inequality is violated by quantum mechanics and could be violated by experimental data provided that the loss of measurement pairs through failure of coincidence is small enough, but the quantitative bound is more restrictive in this case than in the previously analyzed "efficiency loophole".

Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate optical parametric amplifier.

Quantum Cryptography, or more accurately, Quantum Key Distribution (QKD) is based on using an unconditionally secure "quantum channel" to share a secret key among two users. A manufacturer of QKD devices could, intentionally or not, use a (semi-) classical channel instead of the quantum channel, which would remove the supposedly unconditional security. One example is the BB84 protocol, where the quantum channel can be implemented in polarization of single photons. Here, use of several photons instead of one to encode each bit of the key provides a similar but insecure system. For protocols based on violation of a Bell inequality (e.g., the Ekert protocol) the situation is somewhat different. While the possibility is mentioned by some authors, it is generally thought that an implementation of a (semi-) classical channel will differ significantly from that of a quantum channel. Here, a counterexample will be given using an identical physical setup as is used in photon-polarization Ekert QKD. Since the physical implementation is identical, a manufacturer may include this modification as a Trojan Horse in manufactured systems, to be activated at will by an eavesdropper. Thus, the old truth of cryptography still holds: you have to trust the manufacturer of your cryptographic device. Even when you do violate the Bell inequality.

It is well-known in the physics community that the Copenhagen ininterpretation. Usually, a local realistic model is thought to be even further from these two, as in its purest form it can even yield the probabilities from quantum mechanics by the Bell therorem. Nevertheless, by utilizing the "effeciency loophole" such a model can mimic the qauntum probabilities, and more importantly, in this paper it is shown that it is possible to interpret this latter kind of local realistic model such that it contains elements of reality found in the Bohm interpretation, while retaining the complementary present in the Copenhagen interpretation.

Quantum Key Distribution (QKD - also referred to as Quantum Cryptography) is a technique for secret key agreement. It has been shown that QKD rigged with Information-Theoretic Secure (ITS) authentication (using secret key) of the classical messages transmitted during the key distribution protocol is also ITS. Note, QKD without any authentication can trivially be broken by man-in-the-middle attacks. Here, we study an authentication method that was originally proposed because of its low key consumption; a two-step authentication that uses a publicly known hash function, followed by a secret strongly universal2 hash function, which is exchanged each round. This two-step authentication is not information-theoretically secure but it was argued that nevertheless it does not compromise the security of QKD. In the current contribution we study intrinsic weaknesses of this approach under the common assumption that the QKD adversary has access to unlimited resources including quantum memories. We consider one implementation of Quantum Cryptographic protocols that use such authentication and demonstrate an attack that fully extract the secret key. Even including the final key from the protocol in the authentication does not rule out the possibility of these attacks. To rectify the situation, we propose a countermeasure that, while not informationtheoretically secure, restores the need for very large computing power for the attack to work. Finally, we specify conditions that must be satisfied by the two-step authentication in order to restore informationtheoretic security.

This year in Växjö we thought we would try an experiment—it felt high time for a new result. Much of the foundations discussion of previous years has focussed on EPR-style arguments and the meaning and experimental validity of various Bell inequality violations. Yet, there is another pillar of the quantum foundations puzzle that has hardly received any attention in our great series of meetings: It is the phenomenon first demonstrated by Kochen and Specker, quantum contextuality. Recently there has been a rapid growth of activity aimed toward better understanding this aspect of quantum mechanics, which Asher Peres sloganized by the phrase, “unperformed experiments have no results.” Below is a sampling of some important papers on the topic for the reader not yet familiar with the subject. What is the source of this phenomenon? Does it depend only on high level features of quantum mechanics, or is it deep in the conceptual framework on which the theory rests? Might it, for instance, arise from the way quantum mechanics amends the classic laws of probability? What are the mathematically simplest ways contextuality can be demonstrated? How might the known results be made amenable to experimental tests? These were the sorts of discussions we hoped the session would foster.

This paper considers approximations of marginalization sums thatarise in Bayesian inference problems. Optimal approximations ofsuch marginalization sums, using a fixed number of terms, are analyzedfor a simple model. The model under study is motivated byrecent studies of linear regression problems with sparse parametervectors, and of the problem of discriminating signal-plus-noise samplesfrom noise-only samples. It is shown that for the model understudy, if only one term is retained in the marginalization sum, thenthis term should be the one with the largest a posteriori probability.By contrast, if more than one (but not all) terms are to be retained,then these should generally not be the ones corresponding tothe components with largest a posteriori probabilities.

The Kochen-Specker paradox has recently been subject to experimental interest, and in this situation the number of steps in the proof in question is important. The fewer number of steps there are in the proof, the more imperfections can be tolerated in the experimental setup. In the spin-1 version of the Kochen-Specker paradox, when the settings used are directions in three-dimensional space, the proofs can be easily visualized and the steps can easily be counted. In particular, the original Kochen-Specker paradox makes use of so-called great-circle descents. Here, we will examine such descents in detail and also some other versions of the proof for spin-1 systems. We will see that, perhaps contrary to intuition, the proofs that use a small number of steps do not in general use only great-circle descents, and examine the reasons for this and possible extensions. At least one new proof will also be presented for the spin-1 case.

This paper makesan attempt to present Quantum Mechanics in simple terms, butwithout oversimplification. It will be in essence, a comparison ofthe usual understanding of randomness to the more difficult notionof "quantumness." The restricted format of this paper willunfortunately force the presentation to be very terse. But perhapsthis paper can be seen as a synopsis of the approach I have inmind.