Quantum Measurement Principles and Qubit Operations
Explore quantum measurement fundamentals, qubit superposition principles, logic gates, entanglement, and Bell states in a concise manner. Understand the probabilistic and deterministic nature of quantum measurements, as well as the concept of entanglement in qubit systems.
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Presentation Transcript
measurement QUBIT MEASUREMENT = reading of the information through a special equipment to determine the status of the system State of bit before the measurement result of measurement State of bit after the measurement classic case: the measure is deterministic and does not alter the state of the bit 0 0 0 1 1 1 Probabilistic and destructive Quantum measurement State of bit before the measurement result of measurement State of bit after the measurement 0 with probability ?0= |?|2 1 with probability ?1= |?|2 |? = ? |0 |1 |0 + ? |1 Note: it explain the condition |?|2+|?|2= 1; the sum of probability must be 1-
superposition principle 2 QUBIT COMPOUND SYSTEM bit 1/bit2 0 1 2 bit: 4 alternatives 0 00 01 1 10 11 2 qubit: 4 states corresponding to the classic one + superposition principle 2 qubit |01 + ? |?1?2 = ? |00 + ? |10 + ? |11 With ?,?,?,? complex number and |?|2+|?|2+|?|2+|?|2= 1
logic gates 2 QUBIT 2 qubit logic gate |00 + ? |01 + ? |?1?2 = ? |10 + ? |11 G |?1 ?2 = ? |00 + ? |01 + ? |10 + ? |11 With ? ,? ,? ,? linear combination of ?,?,?,?
measurement 2 QUBIT Measurement a measure on the qubit ?1allows us to determine if the first qubit is in |0 or |1 (similarly for ?2), this measure is probabilistic and destructive |?1?2 = ? |00 + ? |01 + ? |10 + ? |11 Examples.
entanglement 2 QUBIT 1 ? = ? = 2 ,? = ? = 0 produced state ?1= ?2 State of bit before the measurement State of bit after the measurement |00 with probability |?|2= 1/2 |01 with probability |?|2= 1/2 result of result of measurement on ?1 0 0 measurement on ?2 0 1 |?1?2 = ? |00 + ? |01 YES NO no correlation between ?1and ?2 1 ? = ? = 2 ,? = ? = 0 entangled state ?1= ?2 State of bit before the measurement State of bit after the measurement |00 with probability |?|2= 1/2 |11 with probability |?|2= 1/2 result of result of measurement on ?1 0 1 measurement on ?2 0 1 |?1?2 = ? |00 + ? |11 YES YES Both the measurement on ?1and ?2is unpredictable perfect correlation between ?1and ?2 When it happens, the two qubit are entangled
Bell States 2 QUBIT Bell States (maximally entangled)
circuit 2 QUBIT How to create entangled states |?1?2 = |01 , |10 , |11 ? Exercise: what is the exit states if
