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Quantum Engineering Year 2: Advanced Quantum Science Month 25Day 694

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Year 2·Month 25·Week 4

Day 694: Quantum Singleton Bound

Day 694 of 2,016~16 min read

Learning Objectives

•**State** the quantum Singleton bound and explain its significance
•**Derive** the bound using quantum information-theoretic arguments
•**Compare** quantum and classical Singleton bounds
•**Identify** codes that saturate the bound (MDS codes)
•**Apply** the bound to verify code parameters are achievable
•**Understand** why the quantum bound is tighter by a factor of 2

Today's Schedule (7 hours)

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On this page

1 The Quantum Singleton Bound Statement of the Bound Physical Interpretation Why Singleton 2 Classical vs Quantum Singleton Bounds Classical Singleton Bound Quantum Singleton Bound The Factor of 2 Difference Example Comparison 3 Derivation of the Quantum Singleton Bound Method 1 Cleaning Lemma Approach Method 2 Entanglement Argument 4 Maximum Distance Separable MDS Codes Definition Properties of MDS Codes Known Quantum MDS Codes Non-MDS Codes 5 The Perfect Five-Qubit Code Stabilizer Generators Logical Operators Why Its Special 6 Proving Code Impossibility Example 1 No 413 Code Example 2 No 623 Code Example 3 Whats Possible for n 9 d 3 7 Beyond the Singleton Bound Tighter Bounds Codes That Beat Singleton Quantum Mechanics Connection Information-Theoretic Perspective The Factor of 2 as Quantum Signature

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