---
title: DensityMatrix (latest version)
description: API reference for qiskit.quantum_info.DensityMatrix in the latest version of qiskit
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.quantum_info.DensityMatrix
---

# DensityMatrix

*class* `qiskit.quantum_info.DensityMatrix(data, dims=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L45-L856)

Bases: `QuantumState`, `TolerancesMixin`

DensityMatrix class

Initialize a density matrix object.

**Parameters**

- **data** (*np.ndarray |* [*list*](https://docs.python.org/3/library/stdtypes.html#list)  *|*[*QuantumCircuit*](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")  *|*[*circuit.instruction.Instruction*](/docs/api/qiskit/qiskit.circuit.Instruction "qiskit.circuit.instruction.Instruction") *| QuantumState*) – A statevector, quantum instruction or an object with a `to_operator` or `to_matrix` method from which the density matrix can be constructed. If a vector the density matrix is constructed as the projector of that vector. If a quantum instruction, the density matrix is constructed by assuming all qubits are initialized in the zero state.
- **dims** ([*int*](https://docs.python.org/3/library/functions.html#int)  *|*[*tuple*](https://docs.python.org/3/library/stdtypes.html#tuple)  *|*[*list*](https://docs.python.org/3/library/stdtypes.html#list) *| None*) – The subsystem dimension of the state (See additional information).

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if input data is not valid.

**Additional Information:**

The `dims` kwarg can be None, an integer, or an iterable of integers.

- `Iterable` – the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list.
- `Int` or `None` – the leading dimension of the input matrix specifies the total dimension of the density matrix. If it is a power of two the state will be initialized as an N-qubit state. If it is not a power of two the state will have a single d-dimensional subsystem.

## Attributes

### atol

Default value: `1e-08`

### data

Return data.

### dim

Return total state dimension.

### num\_qubits

Return the number of qubits if a N-qubit state or None otherwise.

### rtol

Default value: `1e-05`

### settings

Return settings.

## Methods

### conjugate

`conjugate()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L213-L215)

Return the conjugate of the density matrix.

### copy

`copy()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/quantum_state.py#L74-L76)

Make a copy of current operator.

### dims

`dims(qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/quantum_state.py#L70-L72)

Return tuple of input dimension for specified subsystems.

### draw

`draw(output=None, **drawer_args)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L137-L177)

Return a visualization of the density matrix.

**repr**: ASCII TextMatrix of the state’s `__repr__`.

**text**: ASCII TextMatrix that can be printed in the console.

**latex**: An IPython Latex object for displaying in Jupyter Notebooks.

**latex\_source**: Raw, uncompiled ASCII source to generate array using LaTeX.

**qsphere**: Matplotlib figure, rendering of density matrix using plot\_state\_qsphere().

**hinton**: Matplotlib figure, rendering of density matrix using plot\_state\_hinton().

**bloch**: Matplotlib figure, rendering of density matrix using plot\_bloch\_multivector().

**Parameters**

- **output** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – Select the output method to use for drawing the state. Valid choices are repr, text, latex, latex\_source, qsphere, hinton, or bloch. Default is repr. Default can be changed by adding the line `state_drawer = <default>` to `~/.qiskit/settings.conf` under `[default]`.
- **drawer\_args** – Arguments to be passed directly to the relevant drawing function or constructor (TextMatrix(), array\_to\_latex(), plot\_state\_qsphere(), plot\_state\_hinton() or plot\_bloch\_multivector()). See the relevant function under qiskit.visualization for that function’s documentation.

**Returns**

`matplotlib.Figure` or [`str`](https://docs.python.org/3/library/stdtypes.html#str) or `TextMatrix` or `IPython.display.Latex`: Drawing of the density matrix.

**Raises**

[**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError) – when an invalid output method is selected.

### evolve

`evolve(other, qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L305-L342)

Evolve a quantum state by an operator.

**Parameters**

- **other** ([*Operator*](/docs/api/qiskit/qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")  *| QuantumChannel |*[*circuit.instruction.Instruction*](/docs/api/qiskit/qiskit.circuit.Instruction "qiskit.circuit.instruction.Instruction")  *|*[*QuantumCircuit*](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – The operator to evolve by.
- **qargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*] | None*) – a list of QuantumState subsystem positions to apply the operator on.

**Returns**

The output density matrix.

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if the operator dimension does not match the specified QuantumState subsystem dimensions.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

### expand

`expand(other)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L248-L265)

Return the tensor product state other ⊗ self.

**Parameters**

**other** ([*DensityMatrix*](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")) – a quantum state object.

**Returns**

the tensor product state other ⊗ self.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if other is not a quantum state.

### expectation\_value

`expectation_value(oper, qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L399-L420)

Compute the expectation value of an operator.

**Parameters**

- **oper** ([*Operator*](/docs/api/qiskit/qiskit.quantum_info.Operator "qiskit.quantum_info.Operator")) – an operator to evaluate expval.
- **qargs** (*None or* [*list*](https://docs.python.org/3/library/stdtypes.html#list)) – subsystems to apply the operator on.

**Returns**

the expectation value.

**Return type**

[complex](https://docs.python.org/3/library/functions.html#complex)

### from\_instruction

*classmethod* `from_instruction(instruction)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L603-L632)

Return the output density matrix of an instruction.

The statevector is initialized in the state $|{0,\ldots,0}\rangle$ of the same number of qubits as the input instruction or circuit, evolved by the input instruction, and the output statevector returned.

**Parameters**

**instruction** ([*circuit.instruction.Instruction*](/docs/api/qiskit/qiskit.circuit.Instruction "qiskit.circuit.instruction.Instruction")  *|*[*QuantumCircuit*](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")) – instruction or circuit

**Returns**

The final density matrix.

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if the instruction contains invalid instructions for density matrix simulation.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

### from\_int

*static* `from_int(i, dims)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L575-L601)

Return a computational basis state density matrix.

**Parameters**

- **i** ([*int*](https://docs.python.org/3/library/functions.html#int)) – the basis state element.
- **dims** ([*int*](https://docs.python.org/3/library/functions.html#int)  *or*[*tuple*](https://docs.python.org/3/library/stdtypes.html#tuple)  *or*[*list*](https://docs.python.org/3/library/stdtypes.html#list)) – The subsystem dimensions of the statevector (See additional information).

**Returns**

The computational basis state $|i\rangle\!\langle i|$.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

**Additional Information:**

The `dims` kwarg can be an integer or an iterable of integers.

- `Iterable` – the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list.
- `Int` – the integer specifies the total dimension of the state. If it is a power of two the state will be initialized as an N-qubit state. If it is not a power of two the state will have a single d-dimensional subsystem.

### from\_label

*classmethod* `from_label(label)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L539-L573)

Return a tensor product of Pauli X,Y,Z eigenstates.

| Label | Statevector                                                 |
| ----- | ----------------------------------------------------------- |
| `"0"` | $\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}$              |
| `"1"` | $\begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}$              |
| `"+"` | $\frac{1}{2}\begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}$   |
| `"-"` | $\frac{1}{2}\begin{pmatrix} 1 & -1 \\ -1 & 1 \end{pmatrix}$ |
| `"r"` | $\frac{1}{2}\begin{pmatrix} 1 & -i \\ i & 1 \end{pmatrix}$  |
| `"l"` | $\frac{1}{2}\begin{pmatrix} 1 & i \\ -i & 1 \end{pmatrix}$  |

**Parameters**

**label** (*string*) – an eigenstate string ket label (see table for allowed values).

**Returns**

The N-qubit basis state density matrix.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if the label contains invalid characters, or the length of the label is larger than an explicitly specified num\_qubits.

### is\_valid

`is_valid(atol=None, rtol=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L193-L206)

Return True if trace 1 and positive semidefinite.

### measure

`measure(qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/quantum_state.py#L296-L331)

Measure subsystems and return outcome and post-measure state.

Note that this function uses the QuantumStates internal random number generator for sampling the measurement outcome. The RNG seed can be set using the [`seed()`](#qiskit.quantum_info.DensityMatrix.seed "qiskit.quantum_info.DensityMatrix.seed") method.

**Parameters**

**qargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list) *or None*) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

**Returns**

**the pair `(outcome, state)` where `outcome` is the**

measurement outcome string label, and `state` is the collapsed post-measurement state for the corresponding outcome.

**Return type**

[tuple](https://docs.python.org/3/library/stdtypes.html#tuple)

### partial\_transpose

`partial_transpose(qargs)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L839-L856)

Return partially transposed density matrix.

**Parameters**

**qargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)) – The subsystems to be transposed.

**Returns**

The partially transposed density matrix.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

### probabilities

`probabilities(qargs=None, decimals=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L422-L506)

Return the subsystem measurement probability vector.

Measurement probabilities are with respect to measurement in the computation (diagonal) basis.

**Parameters**

- **qargs** (*None or* [*list*](https://docs.python.org/3/library/stdtypes.html#list)) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
- **decimals** (*None or* [*int*](https://docs.python.org/3/library/functions.html#int)) – the number of decimal places to round values. If None no rounding is done (Default: None).

**Returns**

The Numpy vector array of probabilities.

**Return type**

np.array

**Examples**

Consider a 2-qubit product state $\rho=\rho_1\otimes\rho_0$ with $\rho_1=|+\rangle\!\langle+|$, $\rho_0=|0\rangle\!\langle0|$.

```python
from qiskit.quantum_info import DensityMatrix

rho = DensityMatrix.from_label('+0')

# Probabilities for measuring both qubits
probs = rho.probabilities()
print('probs: {}'.format(probs))

# Probabilities for measuring only qubit-0
probs_qubit_0 = rho.probabilities([0])
print('Qubit-0 probs: {}'.format(probs_qubit_0))

# Probabilities for measuring only qubit-1
probs_qubit_1 = rho.probabilities([1])
print('Qubit-1 probs: {}'.format(probs_qubit_1))
```

```text
probs: [0.5 0.  0.5 0. ]
Qubit-0 probs: [1. 0.]
Qubit-1 probs: [0.5 0.5]
```

We can also permute the order of qubits in the `qargs` list to change the qubit position in the probabilities output

```python
from qiskit.quantum_info import DensityMatrix

rho = DensityMatrix.from_label('+0')

# Probabilities for measuring both qubits
probs = rho.probabilities([0, 1])
print('probs: {}'.format(probs))

# Probabilities for measuring both qubits
# but swapping qubits 0 and 1 in output
probs_swapped = rho.probabilities([1, 0])
print('Swapped probs: {}'.format(probs_swapped))
```

```text
probs: [0.5 0.  0.5 0. ]
Swapped probs: [0.5 0.5 0.  0. ]
```

### probabilities\_dict

`probabilities_dict(qargs=None, decimals=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/quantum_state.py#L210-L234)

Return the subsystem measurement probability dictionary.

Measurement probabilities are with respect to measurement in the computation (diagonal) basis.

This dictionary representation uses a Ket-like notation where the dictionary keys are qudit strings for the subsystem basis vectors. If any subsystem has a dimension greater than 10 comma delimiters are inserted between integers so that subsystems can be distinguished.

**Parameters**

- **qargs** (*None or* [*list*](https://docs.python.org/3/library/stdtypes.html#list)) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
- **decimals** (*None or* [*int*](https://docs.python.org/3/library/functions.html#int)) – the number of decimal places to round values. If None no rounding is done (Default: None).

**Returns**

The measurement probabilities in dict (ket) form.

**Return type**

[dict](https://docs.python.org/3/library/stdtypes.html#dict)

### purity

`purity()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L221-L227)

Return the purity of the quantum state.

### reset

`reset(qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L508-L537)

Reset state or subsystems to the 0-state.

**Parameters**

**qargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list) *or None*) – subsystems to reset, if None all subsystems will be reset to their 0-state (Default: None).

**Returns**

the reset state.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

**Additional Information:**

If all subsystems are reset this will return the ground state on all subsystems. If only some subsystems are reset this function will perform evolution by the reset [`SuperOp`](/docs/api/qiskit/qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp") of the reset subsystems.

### reverse\_qargs

`reverse_qargs()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L344-L364)

Return a DensityMatrix with reversed subsystem ordering.

For a tensor product state this is equivalent to reversing the order of tensor product subsystems. For a density matrix $\rho = \rho_{n-1} \otimes ... \otimes \rho_0$ the returned state will be $\rho_0 \otimes ... \otimes \rho_{n-1}$.

**Returns**

the state with reversed subsystem order.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

### sample\_counts

`sample_counts(shots, qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/quantum_state.py#L267-L294)

Sample a dict of qubit measurement outcomes in the computational basis.

**Parameters**

- **shots** ([*int*](https://docs.python.org/3/library/functions.html#int)) – number of samples to generate.
- **qargs** (*None or* [*list*](https://docs.python.org/3/library/stdtypes.html#list)) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

**Returns**

sampled counts dictionary.

**Return type**

[Counts](/docs/api/qiskit/qiskit.result.Counts "qiskit.result.Counts")

Additional Information:

> This function *samples* measurement outcomes using the measure [`probabilities()`](#qiskit.quantum_info.DensityMatrix.probabilities "qiskit.quantum_info.DensityMatrix.probabilities") for the current state and qargs. It does not actually implement the measurement so the current state is not modified.
>
> The seed for random number generator used for sampling can be set to a fixed value by using the state’s [`seed()`](#qiskit.quantum_info.DensityMatrix.seed "qiskit.quantum_info.DensityMatrix.seed") method.

### sample\_memory

`sample_memory(shots, qargs=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/quantum_state.py#L236-L265)

Sample a list of qubit measurement outcomes in the computational basis.

**Parameters**

- **shots** ([*int*](https://docs.python.org/3/library/functions.html#int)) – number of samples to generate.
- **qargs** (*None or* [*list*](https://docs.python.org/3/library/stdtypes.html#list)) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).

**Returns**

list of sampled counts in the order sampled.

**Return type**

np.array

Additional Information:

> This function *samples* measurement outcomes using the measure [`probabilities()`](#qiskit.quantum_info.DensityMatrix.probabilities "qiskit.quantum_info.DensityMatrix.probabilities") for the current state and qargs. It does not actually implement the measurement so the current state is not modified.
>
> The seed for random number generator used for sampling can be set to a fixed value by using the state’s [`seed()`](#qiskit.quantum_info.DensityMatrix.seed "qiskit.quantum_info.DensityMatrix.seed") method.

### seed

`seed(value=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/quantum_state.py#L78-L85)

Set the seed for the quantum state RNG.

### tensor

`tensor(other)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L229-L246)

Return the tensor product state self ⊗ other.

**Parameters**

**other** ([*DensityMatrix*](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")) – a quantum state object.

**Returns**

the tensor product operator self ⊗ other.

**Return type**

[DensityMatrix](#qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if other is not a quantum state.

### to\_dict

`to_dict(decimals=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L634-L718)

Convert the density matrix to dictionary form.

This dictionary representation uses a Ket-like notation where the dictionary keys are qudit strings for the subsystem basis vectors. If any subsystem has a dimension greater than 10 comma delimiters are inserted between integers so that subsystems can be distinguished.

**Parameters**

**decimals** (*None or* [*int*](https://docs.python.org/3/library/functions.html#int)) – the number of decimal places to round values. If None no rounding is done (Default: None).

**Returns**

the dictionary form of the DensityMatrix.

**Return type**

[dict](https://docs.python.org/3/library/stdtypes.html#dict)

**Examples**

The ket-form of a 2-qubit density matrix $rho = |-\rangle\!\langle -|\otimes |0\rangle\!\langle 0|$

```python
from qiskit.quantum_info import DensityMatrix

rho = DensityMatrix.from_label('-0')
print(rho.to_dict())
```

```text
{
    '00|00': (0.4999999999999999+0j),
    '10|00': (-0.4999999999999999-0j),
    '00|10': (-0.4999999999999999+0j),
    '10|10': (0.4999999999999999+0j)
}
```

For non-qubit subsystems the integer range can go from 0 to 9. For example in a qutrit system

```python
import numpy as np
from qiskit.quantum_info import DensityMatrix

mat = np.zeros((9, 9))
mat[0, 0] = 0.25
mat[3, 3] = 0.25
mat[6, 6] = 0.25
mat[-1, -1] = 0.25
rho = DensityMatrix(mat, dims=(3, 3))
print(rho.to_dict())
```

```text
{'00|00': (0.25+0j), '10|10': (0.25+0j), '20|20': (0.25+0j), '22|22': (0.25+0j)}
```

For large subsystem dimensions delimiters are required. The following example is for a 20-dimensional system consisting of a qubit and 10-dimensional qudit.

```python
import numpy as np
from qiskit.quantum_info import DensityMatrix

mat = np.zeros((2 * 10, 2 * 10))
mat[0, 0] = 0.5
mat[-1, -1] = 0.5
rho = DensityMatrix(mat, dims=(2, 10))
print(rho.to_dict())
```

```text
{'00|00': (0.5+0j), '91|91': (0.5+0j)}
```

### to\_operator

`to_operator()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L208-L211)

Convert to Operator

**Return type**

[*Operator*](/docs/api/qiskit/qiskit.quantum_info.Operator "qiskit.quantum_info.operators.operator.Operator")

### to\_statevector

`to_statevector(atol=None, rtol=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L807-L837)

Return a statevector from a pure density matrix.

**Parameters**

- **atol** ([*float*](https://docs.python.org/3/library/functions.html#float)) – Absolute tolerance for checking operation validity.
- **rtol** ([*float*](https://docs.python.org/3/library/functions.html#float)) – Relative tolerance for checking operation validity.

**Returns**

**The pure density matrix’s corresponding statevector.**

Corresponds to the eigenvector of the only non-zero eigenvalue.

**Return type**

[Statevector](/docs/api/qiskit/qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector")

**Raises**

[**QiskitError**](/docs/api/qiskit/exceptions#qiskit.exceptions.QiskitError "qiskit.exceptions.QiskitError") – if the state is not pure.

### trace

`trace()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/quantum_info/states/densitymatrix.py#L217-L219)

Return the trace of the density matrix.