Quantum information - Quiz
Quantum information
  • 1. What is the primary study of quantum mechanics?
A) The storage of classical bits in hardware
B) The evolution of macroscopic classical systems
C) How microscopic physical systems change dynamically
D) The mathematical proof of the uncertainty principle
  • 2. How are quantum systems in quantum information theory typically treated?
A) As exclusively infinite-dimensional systems
B) As identical to classical bit storage units
C) Solely as simulations of harmonic oscillators
D) Abstracted away from real-world counterparts
  • 3. Which mathematical tool describes qubits regardless of their physical implementation?
A) Probability distribution vectors of length n
B) Harmonic oscillator equations
C) Classical binary string logic
D) Density matrices over complex numbers
  • 4. What is a physical example of a qubit in a linear optical quantum computer?
A) A large collection of atoms
B) A photon
C) A trapped ion
D) An electron spin
  • 5. What is a physical example of a qubit in a superconducting quantum computer?
A) A single photon
B) A large collection of atoms
C) A harmonic oscillator
D) A solitary ion
  • 6. How does quantum information theory differ from quantum mechanics regarding system dimensions?
A) It ignores continuous-variable systems entirely
B) It rejects the use of complex numbers
C) It concerns both continuous-variable and finite-dimensional systems
D) It only focuses on infinite-dimensional systems
  • 7. What does entropy measure in a physical system?
A) The number of bits used to store data
B) The momentum of particles
C) The total energy
D) Uncertainty in the state
  • 8. Who laid out the concepts of classical information theory?
A) Albert Einstein
B) Max Planck
C) Richard Feynman
D) Claude Shannon
  • 9. What is the requirement for a system to be a capable bit?
A) Having infinite dimensions
B) Being a photon
C) Being microscopic
D) Having two states
  • 10. How is Shannon entropy defined in relation to measurement?
A) Physical work required to perform measurement
B) Information lost during measurement
C) Information gained after measurement
D) Energy dissipated during measurement
  • 11. In the context of Shannon entropy, what is another way to view the measure?
A) Energy of the discrete distribution
B) Total classical bits available
C) Linearity of the system
D) Uncertainty prior to measurement
  • 12. What are the units of Shannon entropy?
A) Joules
B) Bits
C) Hertz
D) Kelvin
  • 13. What base is the logarithm in the Shannon entropy formula?
A) Base 2
B) Natural logarithm (e)
C) Base 10
D) Base 8
  • 14. When are the interpretations of Shannon entropy usually most meaningful?
A) When the system has only one state
B) When the number of samples is large
C) When the entropy is zero
D) When the system is microscopic
  • 15. What does Shannon entropy quantify regarding information sources?
A) Physical resources required to store output
B) The temperature of the source
C) The speed of data transmission
D) The number of bits in a single sample
  • 16. Which decade saw the development of techniques for manipulating single-atom quantum states?
A) 1990s
B) 1970s
C) 1960s
D) 1980s
  • 17. What caused researchers to consider quantum computing in the context of electronics?
A) The discovery of the Deutsch-Jozsa algorithm
B) The need to disprove relativity
C) Quantum effects causing interference as transistors got smaller
D) The invention of the scanning tunneling microscope
  • 18. What is the basic unit of quantum information?
A) Quark
B) Byte
C) Qubit
D) Bit
  • 19. What is the standard measure used for quantum information?
A) Planck's constant
B) Von Neumann entropy
C) Shannon entropy
D) Boltzmann constant
  • 20. Which of the following fields is mentioned as being involved in quantum information science?
A) Geology
B) Astronomy
C) Cryptography
D) Botany
  • 21. Which century saw the transition from classical physics to quantum physics?
A) 19th century
B) 20th century
C) 21st century
D) 18th century
  • 22. What was the name of the phenomenon where classical physics predicted electrons would spiral into the nucleus?
A) Quantum tunneling
B) Wave-particle duality
C) Photoelectric effect
D) Ultraviolet catastrophe
  • 23. Which scientist formulated quantum mechanics using wave mechanics?
A) John von Neumann
B) Erwin Schrödinger
C) Werner Heisenberg
D) Carl Helstrom
  • 24. Which scientist formulated quantum mechanics using matrix mechanics?
A) Werner Heisenberg
B) Alexander Holevo
C) Ruslan Stratonovich
D) Erwin Schrödinger
  • 25. In which decade did Ruslan Stratonovich, Carl Helstrom, and Gordon propose a formulation of optical communications using quantum mechanics?
A) 1980s
B) 1970s
C) 1950s
D) 1960s
  • 26. Who obtained an upper bound of communication speed for classical messages via a quantum channel?
A) Von Neumann
B) Ruslan Stratonovich
C) Carl Helstrom
D) Alexander Holevo
  • 27. What did scientists initially do to address the absurdities of classical physics before quantum mechanics?
A) Adopted string theory
B) Added ad hoc hypotheses
C) Ignored physics entirely
D) Discarded the nucleus model
  • 28. Who created the analogue to Shannon's noiseless coding theorem for qubits in 1995?
A) Max Planck
B) Ben Schumacher
C) Claude Shannon
D) Leonard Susskind
  • 29. What geometric representation is used to describe the state of a qubit?
A) Density matrix
B) Shannon circle
C) Bloch sphere
D) Hilbert space
  • 30. Which theorem prevents an arbitrary qubit from being copied?
A) No-hiding theorem
B) No-teleportation theorem
C) No-cloning theorem
D) No-broadcast theorem
  • 31. Which theorem states that a qubit cannot be fully converted into classical bits?
A) No-deleting theorem
B) No-teleportation theorem
C) No-cloning theorem
D) No-hiding theorem
  • 32. What concept is cited as the basis for the five theorems of quantum information limits?
A) Entropy
B) Classical bits
C) Unitarity
D) Digital states
  • 33. Which theorem prevents an arbitrary qubit from being deleted?
A) No-deleting theorem
B) No-teleportation theorem
C) No-hiding theorem
D) No-cloning theorem
  • 34. Which theorem prevents an arbitrary qubit from being delivered to multiple recipients?
A) No-broadcast theorem
B) No-teleportation theorem
C) No-hiding theorem
D) No-cloning theorem
  • 35. Which theorem demonstrates the conservation of quantum information?
A) No-hiding theorem
B) No-cloning theorem
C) No-broadcast theorem
D) No-deleting theorem
  • 36. How are classical digital states classified compared to qubits?
A) Probabilistic
B) Discrete
C) Continuous
D) Unitary
  • 37. How are quantum gates described mathematically in relation to the Bloch sphere?
A) Translations
B) Reflections
C) Rotations
D) Projections
  • 38. What type of operators are quantum gates?
A) Hermitian
B) Unitary
C) Non-linear
D) Stochastic
  • 39. What complexity class represents problems efficiently solvable by a quantum computer?
A) PSPACE
B) NP
C) P
D) BQP
  • 40. Which algorithm is famous for factoring numbers in polynomial time?
A) Grover's algorithm
B) Simon's algorithm
C) Deutsch-Jozsa algorithm
D) Shor's algorithm
  • 41. What is the speed-up provided by Grover's search algorithm compared to classical algorithms?
A) Linear
B) Exponential
C) Quadratic
D) Constant
  • 42. In what unit is quantum channel capacity measured?
A) Hertz
B) Baud rate
C) Qubits per second
D) Bits per second
  • 43. Which limit of Rényi entropy corresponds to the Shannon entropy?
A) r approaches 2
B) r approaches 0
C) r approaches 1
D) r approaches infinity
  • 44. Which limit of Rényi entropy corresponds to the Hartley entropy?
A) r approaches 0
B) r approaches 0.5
C) r approaches infinity
D) r approaches 1
  • 45. Which limit of Rényi entropy corresponds to the min-entropy?
A) r approaches 1
B) r approaches infinity
C) r approaches 2
D) r approaches 0
  • 46. What is the formula for Von Neumann entropy involving the trace?
A) tr(log2 rho)
B) tr(rho log2 rho)
C) -log2(tr(rho))
D) -tr(rho log2 rho)
  • 47. In what year was the BB84 scheme developed?
A) 1981
B) 1991
C) 1994
D) 1984
  • 48. How many polarization states does BB84 require?
A) Three
B) Four
C) Eight
D) Two
  • 49. In B92, what happens if Bob chooses the wrong basis to measure?
A) He gets the correct bit
B) He gets the opposite bit
C) He gets a random bit
D) He will not measure anything
  • 50. Who developed the E91 protocol?
A) Gilles Brassard
B) Alice
C) Artur Ekert
D) Charles Bennett
  • 51. What causes quantum decoherence?
A) Use of ancilla qubits
B) Interaction with the environment
C) Perfect isolation of the system
D) Measurement of a single 0 or 1 state
  • 52. What is required for a quantum system to maintain coherence perfectly?
A) Quantum error correction
B) Constant measurement
C) Interaction with the environment
D) Perfect isolation
  • 53. In classical mechanics, what is quantum decoherence compared to?
A) The bit model
B) Energy loss by friction
C) The formulation of error codes
D) Fault-tolerant computation
  • 54. Who first discovered the method of formulating a quantum error correcting code?
A) Albert Einstein
B) Peter Shor
C) Richard Feynman
D) No specific researcher
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