Two entangled particles are separated by a large distance. Alice measures her particle and gets spin-up, instantly determining Bob's particle is spin-down. Does this allow Alice to send a message to Bob faster than light?
AYes — Alice can choose what spin state Bob's particle collapses into by choosing her measurement basis
BNo — Alice gets a random outcome she cannot control, so no information is transmitted; the correlation is only visible when results are compared classically
CNo — the collapse is only apparent; both particles always had definite spins that were just unknown
DYes — Bob can detect Alice's measurement because his particle's state changes instantaneously
Alice cannot control which outcome she gets — it is 50% up and 50% down with equal probability. Without control over the outcome, she cannot encode a message. Bob sees only random results on his end as well. The non-local correlation only becomes visible when both compare their results through a classical (slower-than-light) channel. Option C describes hidden variables, which Bell's theorem rules out — the correlations are stronger than any pre-determined values can explain. Option D is wrong because Bob's individual results are random regardless of whether Alice has measured.
Question 2 Multiple Choice
Which of the following correctly explains why entanglement is treated as a resource in quantum information science?
AEntangled states carry more classical information because they span more degrees of freedom
BEntanglement must be created through physical interaction, cannot be generated by local operations alone, and is consumed when used in protocols like teleportation
CEntanglement allows faster-than-light classical communication when shared between distant parties
DEntangled particles can be cloned and distributed to multiple users, enabling scalable quantum networks
Entanglement is a resource because it has a cost: local operations and classical communication (LOCC) cannot create entanglement from an unentangled state. It must be manufactured through physical interaction, protected against decoherence, and consumed when used. Quantum teleportation uses up a pre-shared entangled pair to transmit a quantum state. Option C is false — entanglement cannot enable FTL communication. Option D contradicts the no-cloning theorem, which prohibits copying arbitrary quantum states.
Question 3 True / False
An entangled pair of particles can generally be described by giving each particle its own individual quantum state.
TTrue
FFalse
Answer: False
This is the defining feature of entanglement: an entangled state cannot be written as a product of individual particle states. The Bell state (1/√2)(|↑↓⟩ + |↓↑⟩) has no separate description for each particle — the state is irreducibly joint. This distinguishes entanglement from classical correlation: in a classical pair, each object still has its own definite properties. In an entangled pair, neither particle has a definite state until measured.
Question 4 True / False
Quantum correlations that violate Bell inequalities require some undetected signal traveling between the particles at the moment of measurement.
TTrue
FFalse
Answer: False
Bell inequality violations rule out local hidden variable theories — they show the correlations are stronger than any model where each particle carries pre-determined values. But the violation does not require any signal between particles. The standard interpretation is that entanglement is a global property of the joint quantum state, not mediated by any propagating influence. Crucially, these correlations cannot be used to transmit information, which is consistent with no-signaling theorems in quantum mechanics.
Question 5 Short Answer
Why can't local operations and classical communication (LOCC) create entanglement between two particles that start out unentangled?
Think about your answer, then reveal below.
Model answer: If two particles start in a product state (unentangled), any local operation on particle 1 only modifies particle 1's state — it cannot introduce quantum correlations with particle 2. Classical communication tells one party about the other's measurement outcomes but doesn't physically connect the particles. Neither operation can introduce the essential quantum feature: a joint quantum state that cannot be factored into separate descriptions for each particle. Entanglement requires physical interaction between the particles (or their joint production from a common quantum source).
This is why entanglement is a genuine resource: it cannot be bootstrapped from nothing using local actions and a phone call. Once generated by physical interaction, it can be distributed but not amplified by LOCC. This is the foundation of the resource theory of entanglement, which quantifies how much entanglement is needed for various quantum information tasks and establishes conversion rates between different entangled states.