arXiv subjects

J. Uffink

Publications and source records attributed to J. Uffink.

3 recordsLinked to original sources

arXiv2010

Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean'

The starting point of the present paper is Bell's notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen's (2007, 2009) analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are (i) the correct understanding of the notions of sufficiency, completeness and redundancy involved; and (ii) the fact that the apparatus settings and measurement outcomes have very different theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell's condition of local causality.

quant-ph↗

arXiv2007

Strengthened Bell inequalities for orthogonal spin directions

We strengthen the bound on the correlations of two spin-1/2 particles (qubits) in separable (non-entangled) states for locally orthogonal spin directions by much tighter bounds than the well-known Bell inequality. This provides a sharper criterion for the experimental distinction between entangled and separable states, and even one which is a necessary and sufficient condition for separability. However, these improved bounds do not apply to local hidden-variable theories, and hence they provide a criterion to test the correlations allowed by local hidden-variable theories against those allowed by separable quantum states. Furthermore, these bounds are stronger than some recent alternative experimentally accessible entanglement criteria. We also address the issue of finding a finite subset of these inequalities that would already form a necessary and sufficient condition for non-entanglement. For mixed state we have not been able to resolve this, but for pure states a set of six inequalities using only three sets of orthogonal observables is shown to be already necessary and sufficient for separability.

quant-ph↗

arXiv1998

Thermodynamic uncertainty relations

Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking, their idea was that a definite temperature can be attributed to a system only if it is submerged in a heat bath, in which case energy fluctuations are unavoidable. On the other hand, a definite energy can only be assigned to systems in thermal isolation, thus excluding the simultaneous determination of its temperature. Rosenfeld extended this analogy with quantum mechanics and obtained a quantitative uncertainty relation in the form (Delta U) (Delta (1/T)) >= k where k is Boltzmann's constant. The two `extreme' cases of this relation would then characterize this complementarity between isolation (U definite) and contact with a heat bath (T definite). Other formulations of the thermodynamical uncertainty relations were proposed by Mandelbrot (1956, 1989), Lindhard (1986) and Lavenda (1987, 1991). This work, however, has not led to a consensus in the literature. It is shown here that the uncertainty relation for temperature and energy in the version of Mandelbrot is indeed exactly analogous to modern formulations of the quantum mechanical uncertainty relations. However, his relation holds only for the canonical distribution, describing a system in contact with a heat bath. There is, therefore, no complementarity between this situation and a thermally isolated system.

cond-mat.stat-mech↗