Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated by Heisenberg's thought experiment using a gamma-ray microscope. Here I show that this common assumption is false: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck's constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg's lower bound for the noise-disturbance product is violated even by a nearly nondisturbing, precise position measuring instrument. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.Comment: Revtex, 6 page

A closer look at the uncertainty relation of position and momentum

We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and sufficient condition for finite standard deviations is given. Finally, a new uncertainty relation is derived and it is shown that the latter cannot be improved.Comment: 3 pages, introduction shortened, content unchange

A volume inequality for quantum Fisher information and the uncertainty principle

Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$det(Cov_\rho(A_h,A_j)) \geq det(- \frac{i}{2} Tr(\rho [A_h,A_j]))$$ gives a bound for the quantum generalized covariance in terms of the commutators $[A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $_{\rho,f}$ be the associated quantum Fisher information. In this paper we conjecture the inequality $$det (Cov_\rho(A_h,A_j)) \geq det (\frac{f(0)}{2} _{\rho,f})$$ that gives a non-trivial bound for any natural number $N$ using the commutators $i[\rho, A_h]$. The inequality has been proved in the cases $N=1,2$ by the joint efforts of many authors. In this paper we prove the case N=3 for real matrices

Gaussian quantum operator representation for bosons

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods

An aminostratigraphy for the British Quaternary based on Bithynia opercula

Aminostratigraphies of Quaternary non-marine deposits in Europe have been previously based on the racemization of a single amino acid in aragonitic shells from land and freshwater molluscs. The value of analysing multiple amino acids from the opercula of the freshwater gastropod Bithynia, which are composed of calcite, has been demonstrated. The protocol used for the isolation of intra-crystalline proteins from shells has been applied to these calcitic opercula, which have been shown to more closely approximate a closed system for indigenous protein residues. Original amino acids are even preserved in bithyniid opercula from the Eocene, showing persistence of indigenous organics for over 30 million years. Geochronological data from opercula are superior to those from shells in two respects: first, in showing less natural variability, and second, in the far better preservation of the intra-crystalline proteins, possibly resulting from the greater stability of calcite. These features allow greater temporal resolution and an extension of the dating range beyond the early Middle Pleistocene. Here we provide full details of the analyses for 480 samples from 100 horizons (75 sites), ranging from Late Pliocene to modern. These show that the dating technique is applicable to the entire Quaternary. Data are provided from all the stratotypes from British stages to have yielded opercula, which are shown to be clearly separable using this revised method. Further checks on the data are provided by reference to other type-sites for different stages (including some not formally defined). Additional tests are provided by sites with independent geochronology, or which can be associated with a terrace stratigraphy or biostratigraphy. This new aminostratigraphy for the non-marine Quaternary deposits of southern Britain provides a framework for understanding the regional geological and archaeological record. Comparison with reference to sites yielding independent geochronology, in combination with other lines of evidence, allows tentative correlation with the marine oxygen isotope record

Integrated global assessment of the natural forest carbon potential

Forests are a substantial terrestrial carbon sink, but anthropogenic changes in land use and climate have considerably reduced the scale of this system1. Remote-sensing estimates to quantify carbon losses from global forests2,3,4,5 are characterized by considerable uncertainty and we lack a comprehensive ground-sourced evaluation to benchmark these estimates. Here we combine several ground-sourced6 and satellite-derived approaches2,7,8 to evaluate the scale of the global forest carbon potential outside agricultural and urban lands. Despite regional variation, the predictions demonstrated remarkable consistency at a global scale, with only a 12% difference between the ground-sourced and satellite-derived estimates. At present, global forest carbon storage is markedly under the natural potential, with a total deficit of 226 Gt (model range = 151–363 Gt) in areas with low human footprint. Most (61%, 139 Gt C) of this potential is in areas with existing forests, in which ecosystem protection can allow forests to recover to maturity. The remaining 39% (87 Gt C) of potential lies in regions in which forests have been removed or fragmented. Although forests cannot be a substitute for emissions reductions, our results support the idea2,3,9 that the conservation, restoration and sustainable management of diverse forests offer valuable contributions to meeting global climate and biodiversity targets