Entanglement between Collective Operators in a Linear Harmonic Chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several non-contiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.Comment: 7 pages, 4 figures, significantly revised version with new results, journal reference adde

Experimenter's Freedom in Bell's Theorem and Quantum Cryptography

Bell's theorem states that no local realistic explanation of quantum mechanical predictions is possible, in which the experimenter has a freedom to choose between different measurement settings. Within a local realistic picture the violation of Bell's inequalities can only be understood if this freedom is denied. We determine the minimal degree to which the experimenter's freedom has to be abandoned, if one wants to keep such a picture and be in agreement with the experiment. Furthermore, the freedom in choosing experimental arrangements may be considered as a resource, since its lacking can be used by an eavesdropper to harm the security of quantum communication. We analyze the security of quantum key distribution as a function of the (partial) knowledge the eavesdropper has about the future choices of measurement settings which are made by the authorized parties (e.g. on the basis of some quasi-random generator). We show that the equivalence between the violation of Bell's inequality and the efficient extraction of a secure key - which exists for the case of complete freedom (no setting knowledge) - is lost unless one adapts the bound of the inequality according to this lack of freedom.Comment: 7 pages, 2 figures, incorporated referee comment

The conditions for quantum violation of macroscopic realism

Why do we not experience a violation of macroscopic realism in every-day life? Normally, no violation can be seen either because of decoherence or the restriction of coarse-grained measurements, transforming the time evolution of any quantum state into a classical time evolution of a statistical mixture. We find the sufficient condition for these classical evolutions for spin systems under coarse-grained measurements. Then we demonstrate that there exist "non-classical" Hamiltonians whose time evolution cannot be understood classically, although at every instant of time the quantum spin state appears as a classical mixture. We suggest that such Hamiltonians are unlikely to be realized in nature because of their high computational complexity.Comment: 4 pages, 2 figures, revised version, journal reference adde

Classical world arising out of quantum physics under the restriction of coarse-grained measurements

Conceptually different from the decoherence program, we present a novel theoretical approach to macroscopic realism and classical physics within quantum theory. It focuses on the limits of observability of quantum effects of macroscopic objects, i.e., on the required precision of our measurement apparatuses such that quantum phenomena can still be observed. First, we demonstrate that for unrestricted measurement accuracy no classical description is possible for arbitrarily large systems. Then we show for a certain time evolution that under coarse-grained measurements not only macrorealism but even the classical Newtonian laws emerge out of the Schroedinger equation and the projection postulate.Comment: 4 pages, 1 figure, second revised and published versio

Logical independence and quantum randomness

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.Comment: 9 pages, 4 figures, published version plus additional experimental appendi

Entanglement between smeared field operators in the Klein-Gordon vacuum

Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. In quantum fields, observables restricted to a region of space define a subsystem. While there are proofs on the existence of local observables that would allow a violation of Bell's inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine-tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. Here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. The introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial (mathematical) points but rather smeared over finite volumes. We first give explicit collective observables whose correlations reveal vacuum entanglement in the Klein-Gordon field. We then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the Compton wavelength of the particle corresponding to the massive Klein-Gordon field.Comment: 21 pages, 11 figure

Quantum Optical Experiments Modeled by Long Short-Term Memory

We demonstrate how machine learning is able to model experiments in quantum physics. Quantum entanglement is a cornerstone for upcoming quantum technologies such as quantum computation and quantum cryptography. Of particular interest are complex quantum states with more than two particles and a large number of entangled quantum levels. Given such a multiparticle high-dimensional quantum state, it is usually impossible to reconstruct an experimental setup that produces it. To search for interesting experiments, one thus has to randomly create millions of setups on a computer and calculate the respective output states. In this work, we show that machine learning models can provide significant improvement over random search. We demonstrate that a long short-term memory (LSTM) neural network can successfully learn to model quantum experiments by correctly predicting output state characteristics for given setups without the necessity of computing the states themselves. This approach not only allows for faster search but is also an essential step towards automated design of multiparticle high-dimensional quantum experiments using generative machine learning models