diff --git a/cirq-core/cirq/linalg/transformations.py b/cirq-core/cirq/linalg/transformations.py
index 1a1b8c257e0..be91bf87688 100644
--- a/cirq-core/cirq/linalg/transformations.py
+++ b/cirq-core/cirq/linalg/transformations.py
@@ -589,12 +589,12 @@ def factor_state_vector(
     slices1 = (slice(None),) * n_axes + pivot[n_axes:]
     slices2 = pivot[:n_axes] + (slice(None),) * (t1.ndim - n_axes)
     extracted = t1[slices1]
-    extracted = extracted / np.sum(abs(extracted) ** 2) ** 0.5
+    extracted = extracted / np.linalg.norm(extracted)
     remainder = t1[slices2]
-    remainder = remainder / np.sum(abs(remainder) ** 2) ** 0.5
+    remainder = remainder / (np.linalg.norm(remainder) * t1[pivot] / abs(t1[pivot]))
     if validate:
         t2 = state_vector_kronecker_product(extracted, remainder)
-        if not predicates.allclose_up_to_global_phase(t2, t1, atol=atol):
+        if not np.allclose(t2, t1, atol=atol):
             if not np.isclose(np.linalg.norm(t1), 1):
                 raise ValueError('Input state must be normalized.')
             raise EntangledStateError('The tensor cannot be factored by the requested axes')
diff --git a/cirq-core/cirq/linalg/transformations_test.py b/cirq-core/cirq/linalg/transformations_test.py
index 6e13fb64d62..b92ff5faa13 100644
--- a/cirq-core/cirq/linalg/transformations_test.py
+++ b/cirq-core/cirq/linalg/transformations_test.py
@@ -613,3 +613,22 @@ def test_default_tolerance():
     # Here, we do NOT specify the default tolerance. It is merely to check that the default value
     # is reasonable.
     cirq.sub_state_vector(final_state_vector, [0])
+
+
+@pytest.mark.parametrize('state_1', [0, 1])
+@pytest.mark.parametrize('state_2', [0, 1])
+def test_factor_state_vector(state_1: int, state_2: int):
+    # Kron two state vectors and apply a phase. Factoring should produce the expected results.
+    n = 12
+    for i in range(n):
+        phase = np.exp(2 * np.pi * 1j * i / n)
+        a = cirq.to_valid_state_vector(state_1, 1)
+        b = cirq.to_valid_state_vector(state_2, 1)
+        c = cirq.linalg.transformations.state_vector_kronecker_product(a, b) * phase
+        a1, b1 = cirq.linalg.transformations.factor_state_vector(c, [0], validate=True)
+        c1 = cirq.linalg.transformations.state_vector_kronecker_product(a1, b1)
+        assert np.allclose(c, c1)
+
+        # All phase goes into a1, and b1 is just the dephased state vector
+        assert np.allclose(a1, a * phase)
+        assert np.allclose(b1, b)
diff --git a/cirq-core/cirq/sim/simulation_product_state.py b/cirq-core/cirq/sim/simulation_product_state.py
index 1338d7ebf7a..c4421b41ec2 100644
--- a/cirq-core/cirq/sim/simulation_product_state.py
+++ b/cirq-core/cirq/sim/simulation_product_state.py
@@ -122,7 +122,7 @@ def _act_on_fallback_(
             gate_opt, (ops.ResetChannel, ops.MeasurementGate)
         ):
             for q in qubits:
-                if op_args.allows_factoring:
+                if op_args.allows_factoring and len(op_args.qubits) > 1:
                     q_args, op_args = op_args.factor((q,), validate=False)
                     self._sim_states[q] = q_args
 
diff --git a/cirq-core/cirq/sim/sparse_simulator_test.py b/cirq-core/cirq/sim/sparse_simulator_test.py
index 1ebef6b4240..ee16e285313 100644
--- a/cirq-core/cirq/sim/sparse_simulator_test.py
+++ b/cirq-core/cirq/sim/sparse_simulator_test.py
@@ -1434,3 +1434,19 @@ def test_unseparated_states_str():
 qubits: (cirq.LineQubit(0), cirq.LineQubit(1))
 output vector: 0.707j|00⟩ + 0.707j|10⟩"""
     )
+
+
+@pytest.mark.parametrize('split', [True, False])
+def test_measurement_preserves_phase(split: bool):
+    c1, c2, t = cirq.LineQubit.range(3)
+    circuit = cirq.Circuit(
+        cirq.H(t),
+        cirq.measure(t, key='t'),
+        cirq.CZ(c1, c2).with_classical_controls('t'),
+        cirq.reset(t),
+    )
+    simulator = cirq.Simulator(split_untangled_states=split)
+    # Run enough times that both options of |110> - |111> are likely measured.
+    for _ in range(20):
+        result = simulator.simulate(circuit, initial_state=(1, 1, 1), qubit_order=(c1, c2, t))
+        assert result.dirac_notation() == '|110⟩'
diff --git a/docs/experiments/textbook_algorithms.ipynb b/docs/experiments/textbook_algorithms.ipynb
index 2287dcc5fad..0949421cf64 100644
--- a/docs/experiments/textbook_algorithms.ipynb
+++ b/docs/experiments/textbook_algorithms.ipynb
@@ -233,7 +233,7 @@
     "print(np.round(bobs_bloch_vector, 3))\n",
     "\n",
     "# Verify they are the same state!\n",
-    "np.testing.assert_allclose(bobs_bloch_vector, message_bloch_vector, atol=1e-7)"
+    "np.testing.assert_allclose(bobs_bloch_vector, message_bloch_vector, atol=1e-6)"
    ]
   },
   {