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. 2018 Sep 18;9:3711. doi: 10.1038/s41467-018-05739-8

Table 2.

Measurements carried out by the agents

Agent Value Measured system Measurement completed at Relevant vectors of measurement basis Heisenberg projectors used for reasoning via (Q)
F¯ r R n:01 headsRtailsR πw=okn:10=(USL1020)okLπw=failn:10=1-πw=okn:10
F z S n:11 SS πz=-12n:10=Sπz=+12n:10=S
W¯ w¯ L¯ n:21 ok¯L ¯=12h¯L ¯-t¯L ¯ π(w¯,z)=(ok,¯-12)n:00=(URLS¯0010)ok¯L ¯Sπ(w¯,z)(ok,¯-12)n:00=1-π(w¯,z)=(ok,¯-12)n:00
W w L n:31 okL=12-12L-+12L π(w¯,w)=(ok,¯ok)n:00=(URLS¯0010)(USL1020)ok¯L ¯okL

Each of the four agents observes a value, defined as the outcome of a measurement on a particular system at a particular time. The measurement basis vectors ok¯L ¯ and okL shown in the last two rows are expressed in terms of states, such as -12L and +12L, which are defined in Table 1. The last column shows the measurement operators that the agents insert into statement A(ii) when reasoning according to Assumption (Q). These operators are given in the Heisenberg picture, referring to the system’s state at a particular time, which is specied by a superscript. The bracket stands for the adjoint of the preceding expression