diff --git a/.coverage b/.coverage
new file mode 100644
index 0000000..875e4ee
Binary files /dev/null and b/.coverage differ
diff --git a/quantum_simulator.py b/quantum_simulator.py
index 25ef6a0..cb62afd 100644
--- a/quantum_simulator.py
+++ b/quantum_simulator.py
@@ -25,7 +25,7 @@
 from __future__ import annotations
 
 from dataclasses import dataclass
-from typing import Dict, Iterable, List, Mapping, Optional, Sequence
+from typing import Dict, Mapping, Optional, Sequence
 
 import numpy as np
 
@@ -53,7 +53,8 @@ def most_likely(self) -> str:
             returning the lexicographically smallest string.
         """
 
-        return max(self.counts.items(), key=lambda item: (item[1], item[0]))[0]
+        best_count = max(self.counts.values())
+        return min(k for k, v in self.counts.items() if v == best_count)
 
     def total_shots(self) -> int:
         """Return the total number of measurement shots."""
diff --git a/tests/test_quantum_simulator.py b/tests/test_quantum_simulator.py
index de7661e..9631593 100644
--- a/tests/test_quantum_simulator.py
+++ b/tests/test_quantum_simulator.py
@@ -133,10 +133,10 @@ def test_pauli_z_then_hadamard(self):
         assert probs["1"] == pytest.approx(1.0, abs=1e-8)
 
     def test_identity_gate(self):
-        I = np.eye(2, dtype=np.complex128)
+        identity = np.eye(2, dtype=np.complex128)
         circuit = QuantumCircuit(1)
         circuit.hadamard(0)
-        circuit.apply_custom(I, [0])
+        circuit.apply_custom(identity, [0])
         probs = circuit.probabilities()
         assert probs["0"] == pytest.approx(0.5, abs=1e-8)
 
@@ -247,3 +247,86 @@ def test_partial_probabilities_normalized(self):
         circuit.hadamard(1)
         probs = circuit.probabilities(qubits=[0])
         assert sum(probs.values()) == pytest.approx(1.0)
+
+
+# ── Additional coverage ────────────────────────────────────────────────────
+
+class TestEmptyQubits:
+    def test_probabilities_empty_list_returns_full_distribution(self):
+        """probabilities(qubits=[]) takes the early-return path and matches full dist."""
+        circuit = QuantumCircuit(2)
+        circuit.hadamard(0)
+        probs_empty = circuit.probabilities(qubits=[])
+        probs_full = circuit.probabilities()
+        for key in probs_full:
+            assert probs_empty[key] == pytest.approx(probs_full[key], abs=1e-8)
+
+    def test_measure_empty_qubits_collapses_to_single_basis_state(self):
+        """measure(qubits=[]) collapses the full state; _collapse_state empty path."""
+        rng = np.random.default_rng(seed=0)
+        circuit = QuantumCircuit(2)
+        circuit.hadamard(0)
+        circuit.cnot(0, 1)
+        result = circuit.measure(qubits=[], shots=1, rng=rng)
+        assert result.total_shots() == 1
+        probs = circuit.probabilities()
+        nonzero = [v for v in probs.values() if v > 1e-9]
+        assert len(nonzero) == 1
+        assert nonzero[0] == pytest.approx(1.0, abs=1e-8)
+
+
+class TestNonSquareUnitary:
+    def test_non_square_matrix_raises(self):
+        """A non-square matrix must raise ValueError (covers the ndim/shape check)."""
+        circuit = QuantumCircuit(1)
+        with pytest.raises(ValueError, match="square"):
+            circuit.apply_custom(np.zeros((2, 3), dtype=complex), [0])
+
+
+class TestMostLikelyTieBreaking:
+    def test_tie_broken_by_lexicographically_smallest(self):
+        """Ties in counts must resolve to the lexicographically smallest string."""
+        result = MeasurementResult(counts={"01": 5, "10": 5})
+        assert result.most_likely() == "01"
+
+    def test_tie_three_way(self):
+        result = MeasurementResult(counts={"11": 3, "00": 3, "01": 3})
+        assert result.most_likely() == "00"
+
+
+class TestAdditionalCircuits:
+    def test_pauli_y_gate(self):
+        """Pauli-Y: Y|0⟩ = i|1⟩, so probability of measuring |1⟩ is 1."""
+        Y = np.array([[0, -1j], [1j, 0]], dtype=np.complex128)
+        circuit = QuantumCircuit(1)
+        circuit.apply_custom(Y, [0])
+        probs = circuit.probabilities()
+        assert probs["0"] == pytest.approx(0.0, abs=1e-8)
+        assert probs["1"] == pytest.approx(1.0, abs=1e-8)
+
+    def test_five_qubit_ghz_state(self):
+        """5-qubit GHZ state: equal superposition of |00000⟩ and |11111⟩."""
+        circuit = QuantumCircuit(5)
+        circuit.hadamard(0)
+        for i in range(1, 5):
+            circuit.cnot(0, i)
+        probs = circuit.probabilities()
+        assert probs["00000"] == pytest.approx(0.5, abs=1e-8)
+        assert probs["11111"] == pytest.approx(0.5, abs=1e-8)
+        for key, val in probs.items():
+            if key not in ("00000", "11111"):
+                assert val == pytest.approx(0.0, abs=1e-8)
+
+    def test_bell_state_qubit1_collapses_qubit0(self):
+        """Measuring qubit 0 of a Bell state collapses qubit 1 to the same value."""
+        circuit = QuantumCircuit(2)
+        circuit.hadamard(0)
+        circuit.cnot(0, 1)
+        rng = np.random.default_rng(seed=999)
+        result = circuit.measure(qubits=[0], shots=1, rng=rng)
+        outcome = result.most_likely()
+        probs = circuit.probabilities()
+        if outcome == "0":
+            assert probs["00"] == pytest.approx(1.0, abs=1e-8)
+        else:
+            assert probs["11"] == pytest.approx(1.0, abs=1e-8)