Navigation between quantum states by quantum mirrors

TL;DR

This paper presents an analytical method using quantum Householder reflections to connect any two quantum states, pure or mixed, in an N-state system, enabling precise quantum state navigation.

Contribution

It introduces a compact, exact technique employing quantum Householder reflections for arbitrary quantum state transformations, including mixed states, with practical synthesis recipes.

Findings

Any two pure states can be connected with a single generalized QHR.

Transforming between mixed states with the same invariants requires N QHRs.

Proposes methods to synthesize arbitrary mixed states using QHRs and incoherent processes.

Abstract

We introduce a technique that allows one to connect any two arbitrary (pure or mixed) superposition states of an N-state quantum system. The proposed solution to this inverse quantum mechanical problem is analytical, exact, and very compact. The technique uses standard and generalized quantum Householder reflections (QHRs), which require external pulses of precise areas and frequencies. We show that any two pure states can be linked by just a single generalized QHR. The transfer between any two mixed states with the same dynamic invariants (e.g., the same density matrix eigenvalues) requires in general N QHRs. Moreover, we propose recipes for synthesis of arbitrary preselected mixed states using a combination of QHRs and incoherent processes (pure dephasing or spontaneous emission).