This checkbox should synchronize between open tabs:
Source code

<!doctype html>
<html>
<head>
    <style>html { font-family:Arial }</style>
</head>
<body>
    This checkbox should synchronize between open tabs: <input type="checkbox" id="checkbox" />

    <script>
        function updateCheckbox() {
            document.getElementById('checkbox').checked = (localStorage.checked === 'true');
        }
        updateCheckbox();

        document.getElementById('checkbox').addEventListener('change', function () {
            localStorage.checked = this.checked;
        });

        window.addEventListener('storage', function () {
            updateCheckbox();
        });
    </script>
</body>
</html>