A210532 Minimum number of observables that need to be measured in order to uniquely determine an n-dimensional quantum state that is known a priori to be pure.

3, 7, 9, 15, 17, 22

Offset

2,1

Links

Table of n, a(n) for n=2..7.

Teiko Heinosaari, Luca Mazzarella, and Michael M. Wolf, Quantum Tomography under Prior Information. Communications in Mathematical Physics, 318:355-374, 2013.

Formula

23 <= a(8) <= 24

4n - 5 - log_2(n) <= a(n) <= 4n - 5 for all n >= 2. More precise bounds are given in the Heinosaari paper.

Example

In the n = 2 case, you need to measure all a(2) = 3 linearly independent observables (e.g., the Pauli X, Y, and Z operators) in order to uniquely specify all pure states.

Crossrefs

Sequence in context: A199919 A346303 A178207 * A110872 A032424 A280861

Adjacent sequences: A210529 A210530 A210531 * A210533 A210534 A210535

Keyword

nonn,more

Author

Nathaniel Johnston, Jan 28 2013

Status

approved