Monogamy of Bell's inequality violations in non-signaling theories

We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the non-signaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes and measurement settings. The method is simple, efficient and does not require linear programming. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.Comment: 4 pages, 2 figures, published versio

Correspondence between continuous variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system of arbitrary dimension. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite dimensional Hilbert space and thus can be considered as a universal resource of entanglement. As an explicit example of the formalism a two-mode CV entangled state is mapped onto a two-qutrit entangled state.Comment: 4 pages, 1 figure, revised version, an example adde

Joint reality and Bell inequalities for consecutive measurements

Some new Bell inequalities for consecutive measurements are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism assumption substitutes the non-invasive hypothesis advantageously, provided that the system satisfies the perfect correlation property. The new inequalities are violated quantically. This violation can be expected to be more severe than in the case of precedent temporal Bell inequalities. Some microscopic and mesoscopic situations, in which the new inequalities could be tested, are roughly considered.Comment: 7 pages, no figure

Bell's experiment with intra- and inter-pair entanglement: Single-particle mode entanglement as a case study

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large many-body system where all the pairs are generally entangled with each other. Using an explicit example based on single mode entanglement and an ancillary Bose-Einstein condensate, we show that the Bell-inequality violation in such systems can display statistical properties that are remarkably different from those obtained using identically prepared, independent pairs. In particular, one can have probabilistic violation of Bell's inequalities in which a finite fraction of all the runs result in violation, even though there could be no violation when averaging over all the runs. Whether or not a particular run of results will end up being local realistically explainable is "decided" by a sequence of quantum (random) outcomes.Comment: 7 pages (two column), 5 figure

Operationally Invariant Information in Quantum Measurements

A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only feature known before an experiment is performed are the probabilities for various events to occur. The sum of the individual measures of information for mutually complementary observations is invariant under the choice of the particular set of complementary observations and conserved if there is no information exchange with an environment. That operational quantum information invariant results in N bits of information for a system consisting of N qubits.Comment: 4 pages, 1 figur

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

Quantum and Classical Phases in Optomechanics

The control of quantum systems requires the ability to change and read-out the phase of a system. The non-commutativity of canonical conjugate operators can induce phases on quantum systems, which can be employed for implementing phase gates and for precision measurements. Here we study the phase acquired by a radiation field after its radiation pressure interaction with a mechanical oscillator, and compare the classical and quantum contributions. The classical description can reproduce the nonlinearity induced by the mechanical oscillator and the loss of correlations between mechanics and optical field at certain interaction times. Such features alone are therefore insufficient for probing the quantum nature of the interaction. Our results thus isolate genuine quantum contributions of the optomechanical interaction that could be probed in current experiments.Comment: 10 pages, 3 figure

Creating and probing macroscoping entanglement with light

We describe a scheme showing signatures of macroscopic optomechanical entanglement generated by radiation pressure in a cavity system with a massive movable mirror. The system we consider reveals genuine multipartite entanglement. We highlight the way the entanglement involving the inaccessible massive object is unravelled, in our scheme, by means of field-field quantum correlations.Comment: 4 pages, 5 figure, RevTeX

Crucial Role of Quantum Entanglement in Bulk Properties of Solids

We demonstrate that the magnetic susceptibility of strongly alternating antiferromagnetic spin-1/2 chains is an entanglement witness. Specifically, magnetic susceptibility of copper nitrate (CN) measured in 1963 (Berger et al., Phys. Rev. 132, 1057 (1963)) cannot be described without presence of entanglement. A detailed analysis of the spin correlations in CN as obtained from neutron scattering experiments (Xu et al., Phys. Rev. Lett. 84, 4465 (2000)) provides microscopic support for this interpretation. We present a quantitative analysis resulting in the critical temperature of 5K in both, completely independent, experiments below which entanglement exists.Comment: 4 pages, 2 figure