Quantum cryptography is the science of exploiting quantum mechanical properties such as quantum entanglement, measurement disturbance, no-cloning theorem, and the principle of superposition to perform various cryptographic tasks. Historically defined as the practice of encoding messages, a concept now referred to as encryption, quantum cryptography plays a crucial role in the secure processing, storage, and transmission of information across various domains.

One aspect of quantum cryptography is quantum key distribution (QKD), which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical (i.e. non-quantum) communication. Furthermore, quantum cryptography affords the authentication of messages, which allows the legitimates parties to prove that the messages were not wiretaped during transmission. For example, in a cryptographic set-up, it is impossible to copy with perfect fidelity, the data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed due to wave function collapse (no-cloning theorem). This could be used to detect eavesdropping in QKD schemes, or in quantum communication links and networks. These advantages have significantly influenced the evolution of quantum cryptography, making it practical in today's digital age, where devices are increasingly interconnected and cyberattacks have become more sophisticated. As such quantum cryptography is a critical component in the advancement of a quantum internet, as it establishes robust mechanisms to ensure the long-term privacy and integrity of digital communications and systems.

In the early 1970s, Stephen Wiesner, then at Columbia University in New York, introduced the concept of quantum conjugate coding. His seminal paper titled "Conjugate Coding" was rejected by the IEEE Information Theory Society but was eventually published in 1983 in SIGACT News. In this paper he showed how to store or transmit two messages by encoding them in two "conjugate observables", such as linear and circular polarization of photons, so that either, but not both, properties may be received and decoded. It was not until Charles H. Bennett, of the IBM's Thomas J. Watson Research Center, and Gilles Brassard met in 1979 at the 20th IEEE Symposium on the Foundations of Computer Science, held in Puerto Rico, that they discovered how to incorporate Wiesner's findings. "The main breakthrough came when we realized that photons were never meant to store information, but rather to transmit it." In 1984, building upon this work, Bennett and Brassard proposed a method for secure communication, which is now called BB84, the first Quantum Key Distribution system. Independently, in 1991 Artur Ekert proposed to use Bell's inequalities to achieve secure key distribution. Ekert's protocol for the key distribution, as it was subsequently shown by Dominic Mayers and Andrew Yao, offers device-independent quantum key distribution.

Companies that manufacture quantum cryptography systems include MagiQ Technologies, Inc. (Boston), ID Quantique (Geneva), QuintessenceLabs (Canberra, Australia), Toshiba (Tokyo), QNu Labs (India) and SeQureNet (Paris).

Cryptography is the strongest link in the chain of data security. However, interested parties cannot assume that cryptographic keys will remain secure indefinitely. Quantum cryptography has the potential to encrypt data for longer periods than classical cryptography. Using classical cryptography, scientists cannot guarantee encryption beyond approximately 30 years, but some stakeholders could use longer periods of protection. Take, for example, the healthcare industry. As of 2017, 85.9% of office-based physicians are using electronic medical record systems to store and transmit patient data. Under the Health Insurance Portability and Accountability Act, medical records must be kept secret. Quantum key distribution can protect electronic records for periods of up to 100 years. Also, quantum cryptography has useful applications for governments and militaries as, historically, governments have kept military data secret for periods of over 60 years. There also has been proof that quantum key distribution can travel through a noisy channel over a long distance and be secure. It can be reduced from a noisy quantum scheme to a classical noiseless scheme. This can be solved with classical probability theory. This process of having consistent protection over a noisy channel can be possible through the implementation of quantum repeaters. Quantum repeaters have the ability to resolve quantum communication errors in an efficient way. Quantum repeaters, which are quantum computers, can be stationed as segments over the noisy channel to ensure the security of communication. Quantum repeaters do this by purifying the segments of the channel before connecting them creating a secure line of communication. Sub-par quantum repeaters can provide an efficient amount of security through the noisy channel over a long distance.

Quantum cryptography is a general subject that covers a broad range of cryptographic practices and protocols. While encryption techniques are widely recognized and understood, a significant challenge remains in the secure distribution of shared keys, often referred to as key establishment or key agreement. Quantum Key Distribution (QKD) aims to address this particular challenge. Below, we explore various notable methodologies and applications currently employed in quantum cryptography.

The best-known and developed application of quantum cryptography is QKD, which is the process of using quantum communication to establish a shared key between two parties (Alice and Bob, for example) without a third party (Eve) learning anything about that key, even if Eve can eavesdrop on all communication between Alice and Bob. If Eve tries to learn information about the key being established, discrepancies will arise causing Alice and Bob to notice. Once the key is established, it is then typically used for encrypted communication using classical techniques. For instance, the exchanged key could be used for symmetric cryptography (e.g. one-time pad).

The security of quantum key distribution can be proven mathematically without imposing any restrictions on the abilities of an eavesdropper, something not possible with classical key distribution. This is usually described as "unconditional security", although there are some minimal assumptions required, including that the laws of quantum mechanics apply and that Alice and Bob are able to authenticate each other, i.e. Eve should not be able to impersonate Alice or Bob as otherwise a man-in-the-middle attack would be possible.