Research

Non-classical correlations

☆Joint operations on non-commuting observables

Quantum mechanics describes physical properties in terms of states and operators. Unless a precise measurement is performed, it is difficult to identify the effects of a property with a specific (eigen-)value of that property. However, quantum statistics often involves statistical correlations between properties that cannot be measured jointly. One well-known example is the case of entangled states, where all physical properties of one system can be perfectly correlated with all physical properties of another system. It is then possible to explore correlations between non-commuting properties by using the remote system as a kind of reference. Similar effects are exploited in quantum
networks to achieve higher precision or more efficient processes for quantum computation. In our group, we are searching for new ways to explore the physics of non-classical correlations.

☆Investigation of operator statistics in quantum processes

One approach towards a better understanding of non-classical correlations is the theoretical analysis of quantum protocols based on the statistics described by operators. In recent work, we have shown that quantum correlations play a very specific role in both quantum teleportation and quantum cloning, where they replace the roles that
classical correlations would play if these processes were applied to classical statistics. We can show that neither teleportation nor cloning should be interpreted as a process that copies the "state". Instead, teleportation and cloning actially copy the values of all physical properties equally. A proper description of quantum fluctuations is therefore essential for our understanding of non-classical correlations.

☆Direct observation of non-classical correlations by sequential measurements

In quantum measurements, an error free measurement of two non-commuting observables is impossible, since the most precise measurements are projections onto eigenstates, and there are no joint eigenstates for non-commuting observables. Experimentally, this means that a measurement of one observable must necessarily disturb the values of the other, so as to introduce the theoretically predicted errors in a final measurement of this property. However, this does not mean that the non-classical correlations are lost - they are merely modified (and usually weakened)
by the statistical noise that characterizes the back-action. It is therefore possible to directly identify the non-classical correlations in the actual measurement data obtained from a sequential measurement. The concept is shown in figure 1: the sequential measurement returns two results, (a,b), corresponding to a simultaneous assignment of eigenvalues to two operators A and B. However, there is a statsitical background noise caused by the finite resultion of the measurement of A and the back-action that sometimes changes the value of B. As we have shown in our research, it is sometimes possible to identify the precise magnitude and pattern of this error background, so that the signal of
non-classical correlations can be separated from the noise of the measurement uncertainties in an almost classical manner.

 

	Overview of our research
	What is so special about quantum physics ?
Optical quantum networks	Non-classical correlations	Explanation of quantum phenomena