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The method that provides identity federation is AWS Single Sign-On (SSO) to connect with identity providers. This approach allows users to authenticate with their existing credentials from other identity providers, enabling seamless access to AWS resources without the need to create separate AWS Identity and Access Management (IAM) accounts. AWS SSO directly supports various identity providers using the Security Assertion Markup Language (SAML), enabling organizations to integrate their existing identity management solutions with AWS services.

Federating identity in this manner enhances user productivity by simplifying access management and improving security through the use of trusted identity sources. It allows for easier management and automation of access controls across AWS environments by leveraging existing corporate identities, eliminating the overhead of managing multiple accounts.

Other methods mentioned do not provide identity federation in the same way. For instance, implementing LDAP authentication is more of a direct authentication mechanism rather than a federation approach. Creating IAM roles for users allows for defining permissions and access, but it does not inherently facilitate the use of external identity providers. Using AWS Lambda for authentication is also not a direct identity federation method; Lambda functions can be used to execute code but do not provide a full identity federation solution.