Chapter 11 Further Reading: Tensor Products and Composite Systems

Textbooks

Sakurai, J. J., & Napolitano, J. J. Modern Quantum Mechanics (3rd ed., Cambridge University Press, 2021). Chapter 6 covers addition of angular momenta and the tensor product formalism. Sakurai's treatment of the EPR problem and Bell inequalities (Chapter 3) is especially clear.
Griffiths, D. J., & Schroeter, D. F. Introduction to Quantum Mechanics (3rd ed., Cambridge University Press, 2018). Section 12.1 introduces the tensor product with an emphasis on two-particle systems. The treatment is concrete and accessible.
Cohen-Tannoudji, C., Diu, B., & Laloe, F. Quantum Mechanics (Wiley, 1977). Volume 1, Complement $D_{IV}$ provides a rigorous mathematical treatment of the tensor product. Volume 2 covers addition of angular momenta extensively.

Nielsen, M. A., & Chuang, I. L. Quantum Computation and Quantum Information (10th Anniversary ed., Cambridge University Press, 2010). The definitive reference for this chapter. Chapter 2 covers the tensor product, Schmidt decomposition, and density matrices. Chapters 1 and 12 cover teleportation, superdense coding, and entanglement as a resource. Every student of quantum information should own this book.
Wilde, M. M. Quantum Information Theory (2nd ed., Cambridge University Press, 2017). More advanced and mathematical than Nielsen & Chuang. Chapters 3–5 cover the Schmidt decomposition, entanglement measures, and the partial trace with full rigor. Freely available on arXiv: arXiv:1106.1445.
Preskill, J. Quantum Computation (Caltech lecture notes). Chapter 4 on quantum entanglement is outstanding. Freely available at http://theory.caltech.edu/~preskill/ph219/.
Bengtsson, I., & Zyczkowski, K. Geometry of Quantum States: An Introduction to Quantum Entanglement (2nd ed., Cambridge University Press, 2017). A beautiful geometric approach to entanglement. Advanced but rewarding.

Einstein, A., Podolsky, B., & Rosen, N. "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Physical Review 47, 777–780 (1935). The paper that started the entanglement debate. Short and readable.
Bohr, N. "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Physical Review 48, 696–702 (1935). Bohr's response to EPR. Notoriously difficult to parse, but historically essential.
Schrödinger, E. "Discussion of probability relations between separated systems." Mathematical Proceedings of the Cambridge Philosophical Society 31, 555–563 (1935). The paper where Schrödinger coined the term "entanglement" (Verschränkung).

Bell, J. S. "On the Einstein Podolsky Rosen paradox." Physics 1, 195–200 (1964). Bell's original paper, proving that no local hidden variable theory can reproduce all predictions of quantum mechanics. Remarkably clear and concise.
Bell, J. S. Speakable and Unspeakable in Quantum Mechanics (2nd ed., Cambridge University Press, 2004). Collected papers by Bell on the foundations of quantum mechanics. Essential reading.
Clauser, J. F., Horne, M. A., Shimony, A., & Holt, R. A. "Proposed experiment to test local hidden-variable theories." Physical Review Letters 23, 880–884 (1969). The CHSH inequality — the experimentally testable form of Bell's theorem.

Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K. "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels." Physical Review Letters 70, 1895–1899 (1993). The quantum teleportation protocol.
Bennett, C. H., & Wiesner, S. J. "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states." Physical Review Letters 69, 2881–2884 (1992). The superdense coding protocol.
Ekert, A. K. "Quantum cryptography based on Bell's theorem." Physical Review Letters 67, 661–663 (1991). The E91 quantum key distribution protocol.

Aspect, A., Dalibard, J., & Roger, G. "Experimental test of Bell's inequalities using time-varying analyzers." Physical Review Letters 49, 1804–1807 (1982). The landmark experiment with fast-switching analyzers.
Bouwmeester, D., Pan, J.-W., Mattle, K., Eibl, M., Weinfurter, H., & Zeilinger, A. "Experimental quantum teleportation." Nature 390, 575–579 (1997). First experimental demonstration of quantum teleportation.
Hensen, B., et al. "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres." Nature 526, 682–686 (2015). The first loophole-free Bell test.

Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. "Quantum entanglement." Reviews of Modern Physics 81, 865–942 (2009). The comprehensive review of entanglement theory. Covers entanglement measures, distillation, and the separability problem in depth.
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., & Wehner, S. "Bell nonlocality." Reviews of Modern Physics 86, 419–478 (2014). Thorough review of Bell inequalities and their applications.

Mermin, N. D. "Is the moon there when nobody looks? Reality and the quantum theory." Physics Today 38(4), 38–47 (1985). A beautifully written popular account of the EPR debate and Bell's theorem.
Gilder, L. The Age of Entanglement: When Quantum Physics Was Reborn (Vintage, 2009). Historical narrative of the entanglement story, from Einstein and Bohr through Bell and Aspect.
Zeilinger, A. Dance of the Photons: From Einstein to Quantum Teleportation (Farrar, Straus and Giroux, 2010). A Nobel laureate's account of entanglement experiments and their implications.

Quantum Country by Andy Matuschak and Michael Nielsen: https://quantum.country. An interactive introduction to quantum computing using spaced repetition. The essay on entanglement is excellent.
IBM Qiskit Textbook: https://qiskit.org/textbook. Hands-on tutorials for building and measuring Bell states on real quantum hardware.
Quirk Quantum Simulator: https://algassert.com/quirk. A drag-and-drop quantum circuit simulator. Try building the Bell state circuit (Hadamard + CNOT) and observing the correlations.