2,437 research outputs found
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
Blending industrial blast furnace gas with H 2 enables Acetobacterium woodii to efficiently co-utilize CO, CO2 and H2
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
- …