Probability representation and quantumness tests for qudits and two-mode light states

Abstract

Using the tomographic-probability representation of spin states, the quantum behavior of qudits is examined. For a general j-qudit state, we propose an explicit formula for quantumness witness whose negative average value is incompatible with classical statistical model. The probability representations of quantum and classical (2j + 1)-level systems are compared within the framework of quantumness tests. In view of the Jordan-Schwinger map, the method is extended for checking the quantumness of two-mode light states.

Quantumness and entanglement witnesses

“…Finally, an aspect of interest would be to analyze the relation between the present approach and the definition of classicality based on the positivity of the Glauber-Sudarshan P-representation [18,19]. Such a representation uses the coherent states as a basis, and for this reason has a straightforward semiclassical description [20,21].…”

Defining quantumness via the Jordan product

“…4 still applies. This opens a door to the study of unbounded observables in infinite-dimensional systems, such as coherent states [18,19], superpositions thereof, and the semiclassical limit [20,21].…”

“…As emphasized at the end of section 5, while the characterization (32) is not suitable in the unbounded case, definition 1 in section 4 still applies. This opens a door to the study of unbounded observables in infinite-dimensional systems, such as coherent states [20,21], superpositions thereof, and the semiclassical limit [22,23].…”

Tomographic discord for a system of two coupled nanoelectric circuits

“…We note that optimal discord D opt is the minimum of values between D diag and D sym (see (23)). In addition, to reveal an extent in which our two-qubit approximation keeps to be appropriate, we compute accuracy parameters (33) and (39).…”

“…Clearly, the tomographic approach generalizes the Shannon information theory on the quantum domain in a very natural way. In the past few decades, a wide class of problems in quantum information theory, e.g., revealing new inequalities for Shannon [28] and Rényi entropies [29][30][31], tomographic approach to the Bell-type inequalities [32], quantumness tests [33], quantum correlations and quantum discord [31,[34][35][36], has been investigated in detail [37].…”