quantum communication, quantum entanglement and all that jazz mark m. wilde communication sciences...
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Quantum Communication, Quantum Entanglement and All That Jazz
Quantum Communication, Quantum Entanglement and All That Jazz
Mark M. Wilde
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Communication Sciences Institute,
Ming Hsieh Department of Electrical Engineering,
University of Southern California,
Los Angeles, California 90089
Communication Sciences Institute,
Ming Hsieh Department of Electrical Engineering,
University of Southern California,
Los Angeles, California 90089
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What is a qubit?
A qubit is a quantum system with two degrees of freedom.
Examples
Electron Spin Photon Polarization
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What are qubits good for?
• Simulation of quantum processes such as chemical reactions and molecular dynamics perhaps has the most potential.
• Shor’s algorithm (1994) breaks the public key cryptography algorithm in polynomial time.
• Grover’s algorithm (1997) gives a quadratic speedup for database search.
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What else are qubits good for?
• Quantum Key Distribution
Zeilinger in Innsbruck Furusawa in Tokyo
• Quantum Teleportation
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More on Teleportation
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Tell me more about a qubit
Measurement projects the qubit
A 2D complex vector represents the state of a qubit:
to state w/ prob.
to state w/ prob.
Represent two qubits joined together with the tensor product:
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What can I do to a qubit?
Pauli matrices act on a single qubit:
The Pauli group acts on multiple qubits:
E.g.,
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What can I do to two qubits?
A Controlled-NOT gate acts on two qubits:
Action of CNOT on computational basis:CNOT in an ion trap
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What is Quantum Entanglement?
Quantum entanglement is the resource that fuels a quantum computer or a quantum communication network.
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What is Entanglement useful for?
•Teleportation•Superdense Coding•Quantum Key Distribution•Quantum Computing•Quantum Secret Sharing•Quantum Games•Quantum Lithography•Quantum Sensors
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“Entanglement” by Ruth Bloch (2000)
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Quantum Information and Noise
Alice
Environment Eve correlates with Alice’s qubits and destroys the fragile nature of a quantum state
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Can We Correct Quantum Errors?
Classical Error Correction copies classical information to protect itBUTNo-Cloning Theorem prohibits general
copying of quantum information.What to do?Classical codes learn about errors by
measuring bits BUTMeasuring a quantum state destroys its quantum information.What to do?Classical codes do not accumulate small
errors over time because classical errors are discrete
BUTQuantum errors are continuous and small errors may build up over time.What to do?
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Shor’s Solution
• Measurement projects the encoded qubits and effectively digitizes the errors.
• Use extra ancilla qubits for redundancy
• Perform particular measurements that learn only about errors
Shor, PRA 52, pp. R2493-R2496 (1995).
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Shor Code
Perform measurements that learn only about errorsEncode qubits with ancillas
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Our Research @
Novel forms of Quantum Error Correction
Entanglement-assisted quantum error correctionEntanglement-assisted quantum error correction (Brun, Devetak, Hsieh)
Convolutional entanglement distillationConvolutional entanglement distillation (Wilde, Krovi, Brun)
Decoherence-free subspaces and subsystemsDecoherence-free subspaces and subsystems (Lidar)
Entanglement-assisted quantum convolutional codingEntanglement-assisted quantum convolutional coding (Wilde, Brun)
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Entanglement-Assisted Quantum Error Correction
Brun et al., Science 314, 436-439 (2006).
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Classical Convolutional Coding
Convolutional Coding techniques have application in
cellular deep space communicationand
Viterbi Algorithm is most popular technique for determining errors
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Quantum Convolutional Coding
Forney et al., IEEE Trans. Inf. Theory 53, 865-880 (2007).
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Entanglement-Assisted Quantum Convolutional Coding
Wilde and Brun, In preparation (2007).
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EAQCC Example
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Block Entanglement Distillation
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Convolutional Entanglement Distillation
Wilde et al., arXiv:0708.3699 (2007).
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Conclusion
• Quantum computing and quantum communication are the future of computing and communication
• Quantum error correction is the way to make quantum computing and communication practical
• There is still much to explore in these areas (QEC07@USC)