arXiv subjects
Publications and source records attributed to Miguel Navascues.
We find two two-qubit states such that any number of copies of one state or the other cannot violate the CHSH Bell inequality. However, their tensor product can produce a CHSH violation of at least 2.023. We also identify a CHSH-local state such that two copies of it are CHSH-violating. The tools employed here can be easily adapted to find instances of non-locality activation in arbitrary Bell scenarios.
We study under which conditions it is possible to assert that a joint demolition measurement cannot be simulated by Local Operations and Classical Communication. More concretely, we consider a scenario where two parties, Alice and Bob, send each an unknown state to a third party, Charlie, who in turn interacts with the states in some undisclosed way and then announces an outcome. We show that, under the assumption that Alice and Bob know the dimensionality of their systems, there exist situations where the statistics of the outcomes reveals the nature of Charlie's measurement.
We study scenarios where a finite set of non-demolition von-Neumann measurements are available. We note that, in some situations, repeated application of such measurements allows estimating an infinite number of parameters of the initial quantum state, and illustrate the point with a physical example. We then move on to study how the system under observation is perturbed after several rounds of projective measurements. While in the finite dimensional case the effect of this perturbation always saturates, there are some instances of infinite dimensional systems where such a perturbation is accumulative, and the act of retrieving information about the system increases its energy indefinitely (i.e., we have `Heat Vision'). We analyze this effect and discuss a specific physical system with two dichotomic von-Neumann measurements where Heat Vision is expected to show.
The author cannot grant that Quantum Mechanics satisfies the axioms described here when repeated measurements are at stake. This does not compromise the validity of the conclusions of the previous article "A glance beyond the quantum model", Proc. Roy. Soc. Lond. A 466, 881-890 (2009).
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints. Such problems arise naturally in quantum theory and quantum information science. To solve them, we introduce a hierarchy of semidefinite programming relaxations which generates a monotone sequence of lower bounds that converges to the optimal solution. We also introduce a criterion to detect whether the global optimum is reached at a given relaxation step and show how to extract a global optimizer from the solution of the corresponding semidefinite programming problem.
One of the most important problems in Physics is how to reconcile Quantum Mechanics with General Relativity. Some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favor of a more general theory. However, as the experiments we can perform nowadays are far away from the range of energies where we may expect to observe non-quantum effects, it is difficult to theorize at this respect. Here we propose a fundamental axiom that we believe any reasonable post-quantum theory should satisfy, namely, that such a theory should recover classical physics in the macroscopic limit. We use this principle, together with the impossibility of instantaneous communication, to characterize the set of correlations that can arise between two distant observers. Although several quantum limits are recovered, our results suggest that quantum mechanics could be falsified by a Bell-type experiment if both observers have a sufficient number of detectors.
In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose symmetric extensions with Positive Partial Transpose (PPT) decreases at least as fast as O(1/N^2). From these results, we derive upper bounds on the time and space complexity of the weak membership problem of separability when attacked via algorithms that search for PPT symmetric extensions. Finally, we show how to estimate the error we incur when we approximate the set of separable states by the set of (PPT) N -extendable quantum states in order to compute the maximum average fidelity in pure state estimation problems, the maximal output purity of quantum channels, and the geometric measure of entanglement.
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of efficiently solvable semidefinite programs. We apply this method to derive arbitrarily good approximations to the optimal measure-and-prepare strategy in generic state estimation problems. Finally, we report its performance in combination with the criterion developed by Doherty et al. [1] for the calculation of the entanglement robustness of a relevant family of quantum states whose separability properties were unknown.
The endemic pine, Pinus canariensis, forms one of the main forest ecosystems in the Canary Islands. In this archipelago, pine forest is a mosaic of natural stands (remnants of past forest overexploitation) and artificial stands planted from the 1940's. The genetic makeup of the artificially regenerated forest is of some concern. The use of reproductive material with uncontrolled origin or from a reduced number of parental trees may produce stands ill adapted to local conditions or unable to adapt in response to environmental change. The genetic diversity within a transect of reforested stands connecting two natural forest fragments has been studied with nuclear and chloroplast microsatellites. Little genetic differentiation and similar levels of genetic diversity to the surrounding natural stands were found for nuclear markers. However, chloroplast microsatellites presented lower haplotype diversity in reforested stands, and this may be a consequence of the lower effective population size of the chloroplast genome, meaning chloroplast markers have a higher sensitivity to bottlenecks. Understory natural regeneration within the reforestation was also analysed to study gene flow from natural forest into artificial stands. Estimates of immigration rate into artificially regenerated forest were high (0.68-0.75), producing a significant increase of genetic diversity (both in chloroplast and nuclear microsatellites), which indicates the capacity for genetic recovery for P. canariensis reforestations surrounded by larger natural stands.
We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite hierarchy of conditions necessarily satisfied by any set of quantum correlations. Each of these conditions could be tested using semidefinite programming. We present here new results concerning this hierarchy. We prove in particular that it is complete, in the sense that any set of correlations satisfying every condition in the hierarchy has a quantum representation in terms of commuting measurements. Although our tests are conceived to rule out non-quantum correlations, and can in principle certify that a set of correlations is quantum only in the asymptotic limit where all tests are satisfied, we show that in some cases it is possible to conclude that a given set of correlations is quantum after performing only a finite number of tests. We provide a criterion to detect when such a situation arises, and we explain how to reconstruct the quantum states and measurement operators reproducing the given correlations. Finally, we present several applications of our approach. We use it in particular to bound the quantum violation of various Bell inequalities.
We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Our approach can be used to obtain upper-bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the violations of the Collins et al. inequalities.
We analyze the asymptotic security of the family of Gaussian modulated Quantum Key Distribution protocols for Continuous Variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.
We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in M. Navascues et al., Phys. Rev. Lett. 94, 010502 (2005). Then, we prove that a generalized version of this protocol does not allow to distill a secret key out of bound entangled Gaussian states.
Security bounds for key distribution protocols using coherent and squeezed states and homodyne measurements are presented. These bounds refer to (i) general attacks and (ii) collective attacks where Eve interacts individually with the sent states, but delays her measurement until the end of the reconciliation process. For the case of a lossy line and coherent states, it is first proven that a secure key distribution is possible up to 1.9 dB of losses. For the second scenario, the security bounds are the same as for the completely incoherent attack.