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