The basic unit of information in computing and digital communications is the bit or the binary digit. The bit is commonly expressed with binary values 0 and 1, which represent the classical physical state of a two-state system; off/on, low/high, etc. The bit-based information processing and communication is called classical information. In quantum information, information is encoded in the state of a two-level quantum system. As a key feature of a quantum system is quantum superposition, quantum information is represented by a quantum bit or a qubit whose state can be written as |ψ⟩=α|0⟩+β|1〉. Moreover, multiple qubits may exhibit entanglement, a unique quantum phenomenon. By taking advantage of superposition and entanglement, quantum information processing enables computing and communication paradigms that are not available in classical information. Experimental quantum information requires extremely accurate and precise control of multi-qubit quantum states and is an intense subject of recent research. This class will focus on introducing basic concepts of quantum information science.

Quantum physics

To be determined.

• Quantum Computation and Quantum Information (M.A. Nielsen & I.L. Chuang)
• J. Preskill’s lecture note (http://theory.caltech.edu/~preskill/ph229/)
• D. Merin's lecture note (https://mermin.lassp.cornell.edu/qcomp/CS483.html)

Topics to be covered (tentative)
# Quantum physics vs classical physics
- Stern Gerlach experiment and quantum superposition
- Quantum measurement (what is spin half?)
- Local realism, uncertainty principle, and Einstein-Podolsky-Rosen "paradox"
- Bell's inequality
- Meaning of Bell's inequality violation

# Quantum state
- Pure state vs mixed state
- density matrix
- reduced density matrix and sub-systems
- quantum measurement formalism

# Entanglement
- two-qubit entanglement
- entanglement vs classical correlation
- Bell states and Bell basis
- non-maximally entangled pure states
- Werner states
- decoherence
- maximally entangled mixed states
- entanglement sudden death
- quantifying purity and entanglement (entropy, concurrence, discord, steering)
- separability and negative partial transpose
- non-physical quantum operations
- LOCC and entanglement purification

# Quantum measurement
- Distinguishing orthogonal states
- Distinguishing non-orthogonal states
- POVM
- weak measurement and weak values

# Multipartite and/or multidimensional entanglement
- Bound entanglement
- GHZ state
- W state
- Entanglement witness

# Quantum information processing (very quickly)
- Channel capacity and Holevo bound
- Dense coding and Teleportation
- quantum cryptography
- simple quantum algorithms
- decoherence, quantum error, fault tolerance
- Fisher information
- Heisenberg limit

Regular class lectures