# generate maximally mixed state

**URL:** <https://itensor.discourse.group/t/generate-maximally-mixed-state/67>\
**Category:** ITensor Julia Questions\
**Tags:** julia\
**Created:** [April 21, 2022, 8:42pm UTC](https://itensor.discourse.group/t/generate-maximally-mixed-state/67 "2022-04-21T20:42:24Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![jisutich](https://avatars.discourse-cdn.com/v4/letter/j/e79b87/32.png) [@jisutich](https://itensor.discourse.group/u/jisutich)\
**Post date:** [April 21, 2022, 8:42pm UTC](https://itensor.discourse.group/t/generate-maximally-mixed-state/67/1 "2022-04-21T20:42:24Z")

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Hi,

Is there a way to generate a mixed state of `N` qubits such that the initial density operator of the total system is \begin{pmatrix} 1/2 &0\\0 &1/2\end{pmatrix}^{\otimes N}?

Thanks

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**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [April 21, 2022, 8:50pm UTC](https://itensor.discourse.group/t/generate-maximally-mixed-state/67/2 "2022-04-21T20:50:29Z")

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You could use the following:

```julia
julia> using ITensors

julia> n = 4
4

julia> s = siteinds("Qubit", n);

julia> rho = MPO(s, "Id");

julia> rho = rho ./ 2;

```

The syntax `rho = rho ./ 2` divides each tensor in the MPO by `2` using Julia’s [broadcasting syntax](https://docs.julialang.org/en/v1/manual/arrays/#Broadcasting).

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<div class="post-metadata">

**Author:** ![jisutich](https://avatars.discourse-cdn.com/v4/letter/j/e79b87/32.png) [@jisutich](https://itensor.discourse.group/u/jisutich)\
**Post date:** [April 23, 2022, 3:18pm UTC](https://itensor.discourse.group/t/generate-maximally-mixed-state/67/3 "2022-04-23T15:18:45Z")

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Hi, guys I have a further question. How to realize the time evolution of MPO? I am thinking the case that P\_1U\_n\dots U\_1 \rho U\_1^{\dagger}\dots U\_n^{\dagger}P\_1 where U is some unitary operator and P represents projective measurement.

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<div class="post-metadata">

**Author:** ![jisutich](https://avatars.discourse-cdn.com/v4/letter/j/e79b87/32.png) [@jisutich](https://itensor.discourse.group/u/jisutich)\
**Post date:** [April 23, 2022, 3:20pm UTC](https://itensor.discourse.group/t/generate-maximally-mixed-state/67/4 "2022-04-23T15:20:18Z")

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Oh I just find this [https://github.com/ITensor/ITensors.jl/blob/main/examples/gate\_evolution/mpo\_gate\_evolution.jl](https://github.com/ITensor/ITensors.jl/blob/main/examples/gate_evolution/mpo_gate_evolution.jl), it may be what I need.