e process probabilistic [@pra61_034301].

The main part of our paper is based on the formalism summarized in Section \[sec:formalism\]. Our description is completely independent of the dimensions of the Hilbert-spaces involved, and we do not even need to fix a basis. In Section \[sec:teleport\] we give a general condition for conditional teleportation in terms of the applicable entangled states and joint measurements. In Section \[sec:matching\] we show that partially entangled states are capable of conditional teleportation with fidelity one, but only if the outcome of the measurement performed by Alice and the state shared by the parties “match” each other. Section \[sec:concl\] summarizes our results.

States, channels and antilinear maps {#sec:formalism}
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Consider a bipartite system with subsystems A and B. The subsystems are described by the Hilbert-spaces ${\cal H}_A$ and ${\cal H}_B$, thus the pure states of the system are in ${\cal H}_A\otimes {\cal H}_B$. Let $\dim {\cal
  H}_A=\dim {\cal H}_B=N$. Let $\{|i\rangle_A\}$ and $\{|i\rangle_B\}\ (i=0,\ldots ,N-1)$ denote the computational bases on ${\cal
  H}_A$ and ${\cal H}_B$, and let $$\label{eq:maxent}
|\Psi^+\rangle_{AB}=\frac{1}{\sqrt{N}}\sum_{i=0}^{N-1}|i\rangle_A|i\rangle_B$$ be a maximally entangled state of the system. All other maximally entangled states of the system can be obtained from $|\Psi^+\rangle$ by local unitary transformations. The set of density matrices of system A will be denoted by ${\cal S}_A$. A quantum channel $\$ _A $ is a completely positive, trace-preserving, and hermiticity preserving ${\cal S}_A \rightarrow {\cal S}_A$ map.

Keeping $|\Psi^{(+)}\rangle$ in mind, we may introduce the relative state representation [@pra54_2614] of states and operators on ${\cal H}_A$. Any pure state $|\Psi\rangle_A\in {\cal H}_A$ can be described by an (unnormalized) *index state* $|\Psi^*\rangle_B\in {\cal H}_B$ so that $$\label{eq:relrep_state}
  |\Psi\rangle_A=\, _B\langle \Psi^*|\Psi^+\rangle_{AB}