We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states which can be directly experimentally assessed if two copies of the state were available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarisers or Stern-Gerlach magnets, remain unknown. Furthermore, we also show that in every experimental run access to only one qubit from the macroscopic reference is sufficient to identify entanglement, violate a Bell inequality, and in fact observe all phenomena observable with macroscopic references. Finally, we provide a state-independent entanglement witness solely in terms of random correlations and emphasise how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilised randomness and should find practical applications in experimental confirmation of multi-photon entanglement or space experiments.PACS numbers: 03.65.UdQuantum mechanics imposes no limits on the spatial separation between entangled particles. This naturally leads one to ask whether observers that have never met and do not share a common reference frame can still detect effects of quantum entanglement. One can further ask if in every experimental run each observer's local reference frame needs to be composed of a huge number of somewhat correlated elementary systems (as it is the case for Stern-Gerlach magnets, polarisers, etc.), or if the effects of entanglement can be detected with references composed of only a few systems.Individually both of these questions have been addressed before. It is known that entanglement can be detected, cryptography can be realised, and Bell inequalities can be violated without a shared reference frame [1][2][3][4][5][6][7][8][9][10][11][12][13] and non-classical correlations can also be observed with finite-size references which are to some degree correlated [14][15][16]. Here we simultaneously address both questions and show that observers who have independent reference frames in an unknown state can each use a single spin-1 2 of the reference per experimental run in order to detect entanglement. If the state of the reference can be controlled a single spin-1 2 of it per experimental run will be shown to be sufficient to observe all phenomena that one can observe with macroscopic references in every experimental run.These findings have both practical and fundamental aspects. On the practical side, they show that entanglement detection is possible with independent reference frames and hence observers can save on communication resources [17][18][19][20] or pre-established quantum entanglement [21,22] that would have to be consumed to correlate local reference frames. On the fundamental side, bounded reference frames were discussed in the context of quantum-to-classical transition [14], where it was noted that the lack of perfect reference frames leads to "intrinsic ...

Abstract. In this paper we present a new class of stream ciphers based on a very simple mechanism. The heart of our method is a Feedback with Carry Shift Registers (FCSR) automaton. This automaton is very similar to the classical LFSR generators, except the fact that it performs operations with carries. Its properties are well mastered: proved period, non-degenerated states, good statistical properties, high non-linearity.The only problem to use such an automaton directly is the fact that the mathematical structure (2-adic fraction) can be retrieved from few bits of its output using an analog of the Berlekamp-Massey algorithm.To mask this structure, we propose to use a filter on the cells of the FCSR automaton. Due to the high non-linearity of this automaton, the best filter is simply a linear filter, that is a XOR on some internal states. We call such a generator a Filtered FCSR (F-FCSR) generator.We propose four versions of our generator: the first uses a static filter with a single output at each iteration of the generator (F-FCSR-SF1). A second with an 8 bit output (F-FCSR-SF8). The third and the fourth are similar, but use a dynamic filter depending on the key (F-FCSR-DF1 and F-FCSR-DF8). We give limitations on the use of the static filter versions, in scope of the time/memory/data tradeoff attack. These stream ciphers are very fast and efficient, especially for hardware implementations.

Abstract. We give a multidimensional generalisation of the complete set of Bell-correlation inequalities given by Werner and Wolf in [26], and byẐukowski and Brukner in [27], for the two-dimensional case. Our construction applies for the n parties, two-observables case, where each observable is d-valued. The d d n inequalities obtained involve homogeneous polynomials. They define the facets of a polytope in a complex vector space of dimension d n . We also show that these inequalities are violated by Quantum Mechanics. We exhibit examples in the three-dimensional case.

Abstract. The Feedback with Carry Shift Registers (FCSRs) have been proposed as an alternative to Linear Feedback Shift Registers (LFSRs) for the design of stream ciphers. FCSRs have good statistical properties and they provide a built-in non-linearity. However, two attacks have shown that the current representations of FCSRs can introduce weaknesses in the cipher. We propose a new "ring" representation of FCSRs based upon matrix definition which generalizes the Galois and Fibonacci representations. Our approach preserves the statistical properties and circumvents the weaknesses of the Fibonacci and Galois representations. Moreover, the ring representation leads to automata with a quicker diffusion characteristic and better implementation results. As an application, we describe a new version of F-FCSR stream ciphers.