Proof of the orthogonal measurement conjecture for qubit states

Andreas Keil

Keil, Andreas

The accessible information of general signal states is obtained by performing a generalized measurement. In the case that the signal alphabet consists of two states of a qubit system, it is proved that a von Neumann (orthogonal) measurement is sufficient to reach the accessible information.

Andreas Keil

The accessible information of general signal states is obtained by performing a generalized measurement. In the case that the signal alphabet consists of two states of a qubit system, it is proved that a von Neumann (orthogonal) measurement is sufficient to reach the accessible information.

Jinbo Wang, Qihang Wang, Pengcheng Hou +1 more

We prove Shor's conjecture: an orthogonal measurement maximizes the information obtainable from any two quantum states in finite dimension. We then show that an error constraint can require three outcomes. For a class of full-rank qubit pairs, the best orthogonal basis switches abruptly as the error penalty increases. Near the switch, three outcomes yield more information at the same error than any orthogonal measurement or random mixture of them. The extra outcome distinguishes confidence levels in one guess; every outcome is used.

Časlav Brukner

Yilin Chen, Lin Chen

In this paper, we investigate the number of independent vector variables in an [Formula: see text]-qubit Orthogonal Product Basis (OPB). Here, the term “independent vector variable” refers to a structural element in the construction of a Unextendible Orthogonal Matrix (UOM). Intuitively, since fixing one state [Formula: see text] in a qubit basis [Formula: see text] uniquely determines its orthogonal partner [Formula: see text], we treat the pair as a single degree of freedom — one variable — rather than two. Based on this counting measure, we propose the conjecture that the number is upper bounded by [Formula: see text]. We show that if the number of orthogonal pairs of variables is minimum, then the matrix corresponding to the OPB contains a column consisting of exactly one variable. In this case the conjecture holds. We also demonstrate more OPBs true for the conjecture, when they have a column containing a small number of independent variables.