We propose a new characterization of non-Markovian quantum evolution based on the concept of non-Markovianity degree. It provides an analog of a Schmidt number in the entanglement theory and reveals the formal analogy between quantum evolution and the entanglement theory: Markovian evolution corresponds to a separable state and the non-Markovian one is further characterized by its degree. It enables one to introduce a non-Markovianity witness-an analog of an entanglement witness, and a family of measures-an analog of Schmidt coefficients, and finally to characterize maximally non-Markovian evolution being an analog of the maximally entangled state. Our approach allows us to classify the non-Markovianity measures introduced so far in a unified rigorous mathematical framework.
The paper presents a scheme to detect entanglement arising from the quantum nature of gravity between a spin qubit and photons, using Stokes parameters. One of the crucial tests of the general theory of relativity is the bending of light due to the curvature. Recently, a quantum counterpart of this experiment to test the quantum nature of the gravitational interaction has been proposed, in which the spin-2, massless graviton yields entanglement between matter and a photon sector. Hence, it provides one of the most crucial experimental signatures for testing the quantum nature of gravity in a lab, since only spin-2-induced entanglement can yield the correct deflection of light due to matter. Here, we propose a positive partial-transpose (PPT) witness criterion for witnessing such an entanglement. We scan the entangled states in this context by studying the overlap of the final state, which is proportional to the entanglement phase. We exploit the Stokes observables to measure the photon state and the spins in the matter sector, thereby constructing a witness for the quantum nature of gravity in this setup. To quantify this entanglement, we will couple the photon to a local oscillator, whose phase need to be controlled to probe the orthogonal components of the macroscopic interference in the laser beam. We have shown that for a non-maximally entangled state mediated by the quantum nature of gravity, the witness attains a maximal negativity of
−0.052. Our findings indicate that this witness effectively detects entanglement within the range
0.71≤∣γ∣<1, where
γ is the overlap between the two coherent states of the photon, providing a clear signature of quantum correlations.
Demonstration of entanglements of mobile electrons in solid state conductors using minimal entanglement linear witness from electrical current correlations has been given. However, detection of maximally entangled states and some mixed states is lacking if the witness is based on two cross correlation measurements only. This thesis is trying to detect them with the same number of measurements by investigating nonlinear witnesses which, in principle, should be able to detect more states than a linear witness. This is done theoretically with a generic entangler-detector setup. We found that all entangled states are detectable when considering pure states only but when considering mixed states, there is no improvement compared to a linear witness. This was done using the symmetries between the two operators corresponding to each measurement.