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Unitary Transformations in 3-D Vector Representation of Qutrit States

Vinod K. Mishra

Published Mar 1, 2018• 0 citations
OpenAlex

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The Qutrit state density matrix is of order 3 and depends on 8 parameters in general case. Visualization of this 8-dimensional state space is practically impossible using 8-dimensional vectors commonly used. Recently a 3-dimensional vector representation of the Qutrit state space (also called Invariant Vector Representation) has been proposed [1]. In this work we present the time-evolution of the IVR vectors for the Qutrit Cascade or Ξ-model to emphasize the advantages of the IVR and also relate IVR vectors to well-known stars of the Majorana State Representation (MSR).

arXiv:1910.03664•Oct 8, 2019•0 citations
The evolution of an open system is usually associated with the interaction of the system with an environment. A new method to study the open-type system evolution of a qubit (two-level atom) state is established. This evolution is determined by a unitary transformation applied to the qutrit (three-level atom) state, which defines the qubit subsystems. This procedure can be used to obtain different qubit quantum channels employing unitary transformations into the qutrit system. In particular, we study the phase damping and spontaneous-emission quantum channels. In addition, we mention a proposal for quasiunitary transforms of qubits, in view of the unitary transform of the total qutrit system. The experimental realization is also addressed. The probability representation of the evolution and its information-entropic characteristics are considered.
The Qutrit state density matrix is of order 3 and depends on 8 parameters in general case. Visualization of this 8-dimensional state space is practically impossible using 8-dimensional vectors commonly used. Recently a 3-dimensional vector representation of the Qutrit state space (also called Invariant Vector Representation) has been proposed [1]. In this work we present the time-evolution of the IVR vectors for the Qutrit Cascade or Ξ-model to emphasize the advantages of the IVR and also relate IVR vectors to well-known stars of the Majorana State Representation (MSR).