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The Majorana tetron is a prototypical topological qubit stemming from the ground state degeneracy of a superconducting island hosting four Majorana modes. This degeneracy manifests as an effective non-local spin degree of freedom, whose most paradigmatic signature is the topological Kondo effect. Degeneracies of states with different fermionic parities characterize also minimal Kitaev chains which have lately emerged as a platform to realize and study unprotected versions of Majorana modes, dubbed poor man's Majorana modes. Here, we introduce the ``poor man's Majorana tetron'', comprising four quantum dots coupled via a floating superconducting island. Its charging energy yields non-trivial correlations among the dots, although, unlike a standard tetron, it is not directly determined by the fermionic parity of the Majorana modes. The poor man's tetron displays parameter regions with a two-fold degenerate ground state with odd fermionic parity, that gives rise to an effective Anderson impurity model when coupled to external leads. We show that this system can approach a regime featuring the topological Kondo effect under a suitable tuning of experimental parameters. Therefore, the poor man's tetron is a promising device to observe the non-locality of Majorana modes and their related fractional conductance., Comment: 28 pages, 9 figures

It has proven difficult to distinguish between topological Majorana bound states and nontopological Andreev bound states and to measure the unique properties of the former. In this work, we aim to alleviate this problem by proposing and theoretically analyzing a new type of fusion protocol based on transport measurements in a Majorana box coupled to normal leads. The protocol is based on switching between different nanowire pairs being tunnel coupled to one of the leads. For a Majorana system, this leads to switching between different states associated with parity blockade. The charge being transmitted at each switch provides a measurement of the Majorana fusion rules. Importantly, the result is different for a system with nontopological Andreev bound states. The proposed protocol only requires measuring a DC current combined with fast gate-control of the tunnel couplings., Comment: 10 pages, 7 figures

A Majorana box - two topological superconducting nanowires coupled via a trivial superconductor - is a building block in devices aiming to demonstrate nonabelian physics, as well as for topological quantum computer architectures. We theoretically investigate charge transport through a Majorana box and show that current can be blocked when two Majoranas couple to the same lead, fixing their parity. In direct analogy to Pauli spin blockade in spin qubits, this parity blockade can be used for fast and high-fidelity qubit initialization and readout, as well as for current-based measurements of decoherence times. Furthermore, we demonstrate that transport can distinguish between a clean Majorana box and a disordered box with additional unwanted Majorana or Andreev bound states., Comment: 4 pages, 3 figures + 6 pages supplementary