^{1}

^{1,2}

^{1}

^{2}

We construct the positive invertible map of the mixed states of a single qutrit onto the antisymmetrized bipartite qutrit states (quasifermions). It is shown that using this one-to-one correspondence between qutrit states and states of two three-dimensional quasifermions one may attribute hidden entanglement to a single mixed state of qutrit.

Quantum entanglement [

Naturally it is hard to prepare and maintain maximally entangled states. In order to control the amount of entanglement in quantum systems several measures were proposed. In case of bipartite pure states an entropy of entanglement [

Recently several attempts to study quantum correlations of noncomposite qudit systems were conducted [

The state of a subsystem of a quantum system is defined by an operation called partial trace, taking mean value over states of another subsystem:

Let us consider a space

Let us pick a basis

Now we will consider a system of two three-dimensional quasifermions, antisymmetrized qutrits. Mathematically it is an exterior product, that is, the quotient of the tensor product by the subspace generated by

We will further omit the

As we already mentioned,

The well-known Peres-Horodecki criterion or PPT criterion is a necessary condition for a mixed state to be separable. It states that if the density operator

The entanglement monotone

The monotone is a convex functional:

The functional is an entanglement monotone, that is, it does not increase on average under local quantum operations and classical communication (LOCC).

Most of the entanglement monotones, like distillability monotones and monotones of formation, are immensely difficult to compute. The more easily countable measure of entanglement is called negativity monotone. It is defined as follows:

Now it is possible to show that in case of initial pure states

The previous considerations about pure states negativities prove that for two different mixed states with equal coefficients

In this paper the simplest nontrivial case of quantum correlations inside qutrit was analyzed. It was demonstrated that for arbitrary mixed qutrit state the negativity is nonzero for corresponding virtual bipartite system of antisymmetrized qutrits. Thus the correlations between the degrees of freedom of qutrit emerge. These considerations could be generalized for qudits with more degrees of freedom in a straightforward manner.

The authors declare that there are no competing interests regarding the publication of this paper.