Let the canned tuna in water drain thoroughly in a sieve so the sauce doesn't end up too thin. Slice the cooked, cold turkey fillet with a sharp knife or meat slicer into paper-thin slices.
Place the drained tuna along with the mayonnaise, lemon juice and anchovies in a blender or tall bowl. Blend these ingredients with an immersion blender until a smooth and even sauce forms. Season the mixture well with some freshly ground pepper.
Spread the arugula in an even layer over a flat serving plate or several plates. Arrange the sliced turkey fillet overlapping on the salad so the meat mostly covers the greens.
Pour the smooth sauce generously over the turkey and spread it slightly with the back of a spoon if needed. Finally sprinkle the capers over the dish and serve immediately.