diff --git a/doc/source/index.rst b/doc/source/index.rst
index 37fc6ac..78ad7f1 100644
--- a/doc/source/index.rst
+++ b/doc/source/index.rst
@@ -22,6 +22,7 @@ qutip-jax |version|: Jax-backend for QuTiP
     :caption: User guide
 
     basics.rst
+    metrics.rst
     solver.rst
     autodiff.rst
 
diff --git a/doc/source/metrics.rst b/doc/source/metrics.rst
new file mode 100644
index 0000000..a7b8584
--- /dev/null
+++ b/doc/source/metrics.rst
@@ -0,0 +1,151 @@
+Using JAX with QuTiP Core Metrics and Entropy
+=============================================
+
+This guide demonstrates how to utilize JAX's `grad` and `jit` functionalities with QuTiP's `core.metrics` and `entropy` modules by changing the backend to JAX.
+
+Setting Up the JAX Backend
+--------------------------
+
+To enable JAX as the backend for QuTiP, you need to set the backend to `jax` using the `use_jax_backend` function. This allows you to use JAX's `grad` and `jit` with QuTiP functions.
+
+.. note::
+
+    This feature is not available in a released version of QuTiP. It is only available on an experimental development branch called `dev-major` in QuTiP.
+
+.. code-block:: python
+
+    import qutip
+    import qutip_jax
+
+    # Use JAX as the backend
+    qutip_jax.use_jax_backend()
+
+Using `jax.jit` with QuTiP
+--------------------------
+
+`jax.jit` compiles your function to make it run faster. Here's how to use `jax.jit` with functions from `qutip.core.metrics` and `qutip.entropy`:
+
+### Example with `fidelity` from `qutip.core.metrics`
+
+.. code-block:: python
+
+    import jax
+    from qutip import basis
+    from qutip.core.metrics import fidelity
+    import qutip_jax
+
+    # Use JAX as the backend
+    qutip_jax.use_jax_backend()
+
+    # Define states
+    psi = basis(2, 0).to("jax")
+    phi = basis(2, 1).to("jax")
+
+    # JIT compile the fidelity function
+    jit_fidelity = jax.jit(fidelity)
+
+    # Compute fidelity using JIT compiled function
+    result = jit_fidelity(psi, phi)
+    print("Fidelity:", result)
+
+### Example with `entropy_vn` from `qutip.entropy`
+
+.. code-block:: python
+
+    from qutip import ket2dm
+    from qutip.entropy import entropy_vn
+    import qutip_jax
+
+    # Use JAX as the backend
+    qutip_jax.use_jax_backend()
+
+    # Define a density matrix
+    rho = ket2dm(psi).to("jax")
+
+    # JIT compile the entropy_vn function
+    jit_entropy_vn = jax.jit(entropy_vn)
+
+    # Compute von Neumann entropy using JIT compiled function
+    result = jit_entropy_vn(rho)
+    print("Von Neumann Entropy:", result)
+
+Using `jax.grad` with QuTiP
+---------------------------
+
+`jax.grad` computes the gradient of a function. Here's how to use `jax.grad` with functions from `qutip.core.metrics` and `qutip.entropy`:
+
+### Example with `fidelity` from `qutip.core.metrics`
+
+To compute the gradient, you need a function that returns a scalar. Note that `jax.grad` for `fidelity` does not support `oper` states.
+
+#### Gradient of `fidelity` for Ket/Bra States
+
+.. code-block:: python
+
+    import jax
+    from qutip import basis, fidelity
+    import qutip_jax
+
+    # Use JAX as the backend
+    qutip_jax.use_jax_backend()
+
+    # Define bra and ket states
+    bra_state = basis(2, 0).dag()
+    ket_state = basis(2, 0)
+
+    # Convert to JAX objects
+    bra_state_jax = bra_state.to("jax")
+    ket_state_jax = ket_state.to("jax")
+
+    # Define a fidelity function
+    def fidelity_jax(state1, state2):
+        return fidelity(state1, state2)
+
+    # Compute the gradient of the fidelity function with respect to the first argument
+    grad_fidelity = jax.grad(fidelity_jax, argnums=0)
+
+    # Calculate the gradient
+    grad_result = grad_fidelity(bra_state_jax, ket_state_jax)
+    print("Gradient of Fidelity:", grad_result)
+    
+### Example with `trace_dist` from `qutip.core.metrics`
+
+The `trace_dist` function supports `oper` states for gradient computation.
+
+.. code-block:: python
+
+    from qutip import rand_dm
+    from qutip.core.metrics import trace_dist
+    import qutip_jax
+
+    # Use JAX as the backend
+    qutip_jax.use_jax_backend()
+
+    # Define an operator state
+    oper_state = rand_dm(2)
+    ket_state = basis(2, 0)
+
+    # Convert to JAX object
+    oper_state_jax = oper_state.to("jax")
+    ket_state_jax = ket_state.to("jax")
+   
+    # Define a trace distance function
+    def trace_dist_jax(state1, state2):
+        return trace_dist(state1, state2)
+
+    # Compute the gradient of the trace distance function with respect to the first argument
+    grad_trace_dist = jax.grad(trace_dist_jax, argnums=0)
+
+    # Calculate the gradient
+    grad_result = grad_trace_dist(oper_state_jax, ket_state_jax)
+    print("Gradient of Trace Distance:", grad_result)
+
+Changing Back to Default Backend
+--------------------------------
+
+If you want to switch back to the default backend (NumPy), use the following:
+
+.. code-block:: python
+
+    qutip.settings.core["numpy_backend"] = np
+