Abstract
We adapt an algorithmic approach to the problem of local realism in a bipartite scenario. We assume that local outcomes are simulated by spatially separated universal Turing machines. The outcomes are calculated from inputs encoding information about a local measurement setting and a description of the bipartite system sent to both parties. In general, such a description can encode some additional information not available in quantum theory, i.e., local hidden variables. Using the Kolmogorov complexity of local outcomes we derive an inequality that must be obeyed by any local realistic theory. Since the Kolmogorov complexity is in general uncomputable, we show that this inequality can be expressed in terms of lossless compression of the data generated in such experiments and that quantum mechanics violates it. Finally, we confirm experimentally our findings using pairs of polarisation-entangled photons and readily available compression software. We argue that our approach relaxes the independent and identically distributed (i.i.d.) assumption, namely that individual bits in the outcome bit-strings do not have to be i.i.d.
Highlights
The idea that physical processes can be considered as computations done on some universal machines traces back to Turing and von Neumann [1], and the growth of the computational power allowed for further development of these concepts
Photons are detected by avalanche photo diodes (APDs), and corresponding detection events from the same pair identified by a coincidence unit (CU) if they arrive within ≈ ±3 ns of each other
We could show that this is not possible if one uses a computation paradigm of a local deterministic Turing machine. This has been already extensively researched in quantum information theory, we present a complementary algorithmic approach for an explicit, experimentally testable example
Summary
The idea that physical processes can be considered as computations done on some universal machines traces back to Turing and von Neumann [1], and the growth of the computational power allowed for further development of these concepts This resulted in a completely new approach to science in which the complexity of observed phenomena is closely related to the complexity of computational resources needed to simulate them [2]. Efficient simulation of quantum systems requires a replacement of deterministic universal Turing machines with quantum computers whose states are non-classically correlated. We can estimate K(x) with some efficient lossless compression algorithm C(x) [11] We extend this picture by considering two Turing machines UA (Alice) and UB (Bob), which are spatially separated. We evaluate an approximation to the NID, the Normalized Compression Distance (NCD) [11], using a lossless compression software, in our case the LZMA Utilities, based on the Lempel-Ziv-Markov chain algorithm [14]
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