arXiv subjects

Ämin Baumeler

Publications and source records attributed to Ämin Baumeler.

27 records · Page 2Linked to original sources

arXiv2018

Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?

The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of consequences. First, the usual definitions of randomness depend on a causal structure and turn meaningless. So motivated, we propose an intrinsic, physically motivated measure for the randomness of a string of bits: its length minus its normalized work value, a quantity we closely relate to its Kolmogorov complexity (the length of the shortest program making a universal Turing machine output this string). We test this alternative concept of randomness for the example of non-local correlations, and we end up with a reasoning that leads to similar conclusions as in, but is conceptually more direct than, the probabilistic view since only the outcomes of measurements that can actually all be carried out together are put into relation to each other. In the same context-free spirit, we connect the logical reversibility of an evolution to the second law of thermodynamics and the arrow of time. Refining this, we end up with a speculation on the emergence of a space-time structure on bit strings in terms of data-compressibility relations. Finally, we show that logical consistency, by which we replace the abandoned causality, it strictly weaker a constraint than the latter in the multi-party case.

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arXiv2018

Computational tameness of classical non-causal models

We show that the computational power of the non-causal circuit model, i.e., the circuit model where the assumption of a global causal order is replaced by the assumption of logical consistency, is completely characterized by the complexity class~$\operatorname{\mathsf{UP}}\cap\operatorname{\mathsf{coUP}}$. An example of a problem in that class is factorization. Our result implies that classical deterministic closed timelike curves (CTCs) cannot efficiently solve problems that lie outside of that class. Thus, in stark contrast to other CTC models, these CTCs cannot efficiently solve~$\operatorname{\mathsf{NP-complete}}$ problems, unless~$\operatorname{\mathsf{NP}}=\operatorname{\mathsf{UP}}\cap\operatorname{\mathsf{coUP}}=\operatorname{\mathsf{coNP}}$, which lets their existence in nature appear less implausible. This result gives a new characterization of~$\operatorname{\mathsf{UP}}\cap\operatorname{\mathsf{coUP}}$ in terms of fixed points.

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arXiv2017

Bell Correlations and the Common Future

Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of explaining Bell correlations through a mechanism in that spirit can be read as questioning either the principle or even its basis: causality. In the former case, the principle can be replaced by its quantum version, accepting as a common cause an entangled state, leaving the phenomenon as mysterious as ever on the classical level (on which, after all, it occurs). If, more radically, the causal structure is questioned in principle, closed space-time curves may become possible that, as is argued in the present note, can give rise to non-local correlations if to-be-correlated pieces of classical information meet in the common future --- which they need to if the correlation is to be detected in the first place. The result is a view resembling Brassard and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's relative-state formalism, avoiding "multiple realities."

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arXiv2017

Non-causal computation

Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a novel computing paradigm beyond quantum computing, replacing this assumption by mere logical consistency: We study non-causal circuits, where a fixed time structure within a gate is locally assumed whilst the global causal structure between the gates is dropped. We present examples of logically consistent non- causal circuits outperforming all causal ones; they imply that suppressing loops entirely is more restrictive than just avoiding the contradictions they can give rise to. That fact is already known for correlations as well as for communication, and we here extend it to computation.

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arXiv2016

Device-independent test of causal order and relations to fixed-points

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities --- just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical consistency allows for violating causal inequalities. Here, we show that a classical environment (with which the parties interact), possibly containing loops, is logically consistent if and only if whatever the involved parties do, there is exactly one fixed-point, the latter being representable as a mixture of deterministic fixed-points. We further show that the non-causal view allows for a model of computation strictly more powerful than computation in a world of fixed causal orders.

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arXiv2016

The space of logically consistent classical processes without causal order

Classical correlations without predefined causal order arise from processes where parties manipulate random variables, and where the order of these interactions is not predefined. No assumption on the causal order of the parties is made, but the processes are restricted to be logically consistent under any choice of the parties' operations. It is known that for three parties or more, this set of processes is larger than the set of processes achievable in a predefined ordering of the parties. Here, we model all classical processes without predefined causal order geometrically and find that the set of such processes forms a polytope. Additionally, we model a smaller polytope --- the deterministic-extrema polytope --- where all extremal points represent deterministic processes. This polytope excludes probabilistic processes that must be --- quite unnaturally --- fine-tuned, because any variation of the weights in a decomposition into deterministic processes leads to a logical inconsistency.

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arXiv2014

Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios

Quantum theory in a global space-time gives rise to non-local correlations, which cannot be explained causally in a satisfactory way; this motivates the study of theories with reduced global assumptions. Oreshkov, Costa, and Brukner (2012) proposed a framework in which quantum theory is valid locally but where, at the same time, no global space-time, i.e., predefined causal order, is assumed beyond the absence of logical paradoxes. It was shown for the two-party case, however, that a global causal order always emerges in the classical limit. Quite naturally, it has been conjectured that the same also holds in the multi-party setting. We show that counter to this belief, classical correlations locally compatible with classical probability theory exist that allow for deterministic signaling between three or more parties incompatible with any predefined causal order.

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arXiv2014

Quantum Private Information Retrieval has linear communication complexity

In Private Information Retrieval (PIR), a client queries an n-bit database in order to retrieve an entry of her choice, while maintaining privacy of her query value. Chor, Goldreich, Kushilevitz, and Sudan showed that, in the information-theoretical setting, a linear amount of communication is required for classical PIR protocols (and thus that the trivial protocol is optimal). This linear lower bound was shown by Nayak to hold also in the quantum setting. Here, we extend Nayak's result by considering approximate privacy, and requiring security only against "specious" adversaries, which are, in analogy to classical honest-but-curious adversaries, the weakest reasonable quantum adversaries. We show that, even in this weakened scenario, Quantum Private Information Retrieval (QPIR) requires n qubits of communication. From this follows that Le Gall's recent QPIR protocol with sublinear communication complexity is not information-theoretically private, against the weakest reasonable cryptographic adversary.

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arXiv2014

Perfect signaling among three parties violating predefined causal order

The paradigmatic view where information is seen as a more fundamental concept than the laws of physics leads to a different understanding of spacetime where the causal order of events emerges from correlations between random variables representing physical quantities. In particular, such an information-theoretic approach does not enforce a global spacetime structure. By following this path, we conclude that perfect signaling correlations among three parties are possible which do not obey the restrictions imposed by global spacetime. We show this using a recent framework based on the sole assumptions that locally, quantum theory is valid and random variables can be described by probability distributions. Our result is of zero-error type and is an analog to a tripartite appearance of quantum non-locality which manifests itself by satisfying a condition with certainty whereas the same is impossible for any local theory.

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