Research ArticleQUANTUM INFORMATION

# Experimental verification of an indefinite causal order

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Vol. 3, no. 3, e1602589

### Tables

• Table 1 List of operators performed by the two parties.

The table shows Alice’s four measurement operators and her three repreparation operators, which Alice applies when her outcome is |0〉; when Alice’s outcome is |1〉, Alice performs the identity. Bob’s 10 unitary operators are shown in the third column.

 Alice’s measurement operators Alice’s repreparation operators Bob’s unitary operators (1) (1) (1) (6) (2) (2) (2) (7) (3) (3) (3) (8) (4) (4) (9) (5) (10)
• Table 2 Set of wave plate angles.

A list of all of the wave plate angles used to perform the operators listed in Table 1. In our experiment, all combinations of these settings were used, which, together with our three input states, results in 360 measurement settings.

 Alice’s measurementoperators Alice’s repreparationoperators Bob’s unitaryoperators (1) 0°HWP, 0°QWP (1) 0°HWP, 0°QWP (1) 0°QWP, 0°HWP,0°QWP (2) 22.5°HWP, 45°QWP (2) 22.5°HWP, 0°QWP (2) 0°QWP, 45°HWP,0°QWP (3) 0°HWP, − 45°QWP (3) 0°HWP, − 45°QWP (3) 90°QWP, 45°HWP,0°QWP (4) 45°HWP, 0°QWP (4) 90°QWP, 0°HWP,0°QWP (5) 90°QWP, 0°HWP,45°QWP (6) 90°QWP, 45°HWP,45°QWP (7) 0°QWP, 0°HWP,45°QWP (8) 45°QWP, 0°HWP,90°QWP (9) 45°QWP, 45°HWP,90°QWP (10) 45°QWP, 0°HWP,0°QWP

### Supplementary Materials

section A. Choi-Jamiołkowski isomorphism

fig. S1. Experimentally estimated probabilities.

fig. S2. Experimentally estimated probabilities.

fig. S3. Experimentally estimated probabilities.

table S1. List of all the experimental measurement settings and the corresponding coefficients.

Reference (35)

• ## Supplementary Materials

This PDF file includes:

• section A. Choi-Jamiołkowski isomorphism
• fig. S1. Experimentally estimated probabilities.
• fig. S2. Experimentally estimated probabilities.
• fig. S3. Experimentally estimated probabilities.
• table S1. List of all the experimental measurement settings and the corresponding coefficients.
• Reference (35)