Wigner's friend

Wigner's friend is a thought experiment in theoretical quantum physics, proposed by the physicist Eugene Wigner in 1961. The scenario involves an indirect observation of a quantum measurement: An observer W observes another observer F who performs a quantum measurement on a physical system. The two observers then formulate a statement about the physical system's state after the measurement according to the laws of quantum theory. However, in most of the interpretations of quantum theory, the resulting statements of the two observers contradict each other. This reflects a seeming incompatibility of two laws in quantum theory: the deterministic and continuous time evolution of the state of a closed system and the probabilistic, discontinuous collapse of the state of a system upon measurement. Wigner's friend is therefore directly linked to the measurement problem in quantum mechanics with its famous Schrödinger's cat paradox.The state of the observer's perception is considered to be entangled with the state of the cat. The perception state 'I perceive a live cat' accompanies the 'live-cat' state and the perception state 'I perceive a dead cat' accompanies the 'dead-cat' state. ... It is then assumed that a perceiving being always finds his/her perception state to be in one of these two; accordingly, the cat is, in the perceived world, either alive or dead. ... I wish to make clear that, as it stands, this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat. F 1 {displaystyle F_{1}} measures a qubit state R {displaystyle R} prepared in | ψ ⟩ R = 1 3 | h ⟩ R + 2 3 | t ⟩ R { extstyle |psi angle _{R}={frac {1}{sqrt {3}}}|h angle _{R}+{sqrt {frac {2}{3}}}|t angle _{R}} in the { h , t } {displaystyle {h,t}} - basis and gets h {displaystyle h} ('heads') or t {displaystyle t} ('tails') with probability 1 3 { extstyle {frac {1}{3}}} and 2 3 { extstyle {frac {2}{3}}} , respectively. Depending on this outcome, F 1 {displaystyle F_{1}} prepares a spin system S {displaystyle S} in state | ψ ⟩ S {displaystyle |psi angle _{S}} and sends it to F 2 {displaystyle F_{2}} . Here, | ψ ⟩ S = | ↓ ⟩ S { extstyle |psi angle _{S}=|downarrow angle _{S}} if the outcome was h {displaystyle h} and | ψ ⟩ S = | → ⟩ S = 1 2 | ↑ ⟩ S + 1 2 | ↓ ⟩ S { extstyle |psi angle _{S}=| ightarrow angle _{S}={frac {1}{sqrt {2}}}|uparrow angle _{S}+{frac {1}{sqrt {2}}}|downarrow angle _{S}} if the outcome was t {displaystyle t} . F 2 {displaystyle F_{2}} measures the received spin | ψ ⟩ S {displaystyle |psi angle _{S}} in the { ↑ , ↓ } {displaystyle {uparrow ,downarrow }} - basis. W 1 {displaystyle W_{1}} measures L 1 = R ⊗ F 1 {displaystyle L_{1}=Rotimes F_{1}} in the { | + ⟩ L 1 , | − ⟩ L 1 } {displaystyle {|+ angle _{L_{1}},|- angle _{L_{1}}}} - basis where | + ⟩ L 1 = 1 2 | h ⟩ R | h ⟩ F 1 + 1 2 | t ⟩ R | t ⟩ F 1 { extstyle |+ angle _{L_{1}}={frac {1}{sqrt {2}}}|h angle _{R}|h angle _{F_{1}}+{frac {1}{sqrt {2}}}|t angle _{R}|t angle _{F_{1}}} and | − ⟩ L 1 = 1 2 | h ⟩ R | h ⟩ F 1 − 1 2 | t ⟩ R | t ⟩ F 1 . { extstyle |- angle _{L_{1}}={frac {1}{sqrt {2}}}|h angle _{R}|h angle _{F_{1}}-{frac {1}{sqrt {2}}}|t angle _{R}|t angle _{F_{1}}.} . W 2 {displaystyle W_{2}} measures L 2 = S ⊗ F 2 {displaystyle L_{2}=Sotimes F_{2}} in the { | + ⟩ L 2 , | − ⟩ L 2 } {displaystyle {|+ angle _{L_{2}},|- angle _{L_{2}}}} - basis where | + ⟩ L 2 = 1 2 | ↓ ⟩ S | ↓ ⟩ F 2 + 1 2 | ↑ ⟩ S | ↑ ⟩ F 2 { extstyle |+ angle _{L_{2}}={frac {1}{sqrt {2}}}|downarrow angle _{S}|downarrow angle _{F_{2}}+{frac {1}{sqrt {2}}}|uparrow angle _{S}|uparrow angle _{F_{2}}} and | − ⟩ L 2 = 1 2 | ↓ ⟩ S | ↓ ⟩ F 2 − 1 2 | ↑ ⟩ S | ↑ ⟩ F 2 { extstyle |- angle _{L_{2}}={frac {1}{sqrt {2}}}|downarrow angle _{S}|downarrow angle _{F_{2}}-{frac {1}{sqrt {2}}}|uparrow angle _{S}|uparrow angle _{F_{2}}} .The measurement outcomes of W 1 {displaystyle W_{1}} and W 2 {displaystyle W_{2}} are compared: If both got m i n u s {displaystyle minus} the experiment is halted. Otherwise, the protocol starts at the initial step again. Wigner's friend is a thought experiment in theoretical quantum physics, proposed by the physicist Eugene Wigner in 1961. The scenario involves an indirect observation of a quantum measurement: An observer W observes another observer F who performs a quantum measurement on a physical system. The two observers then formulate a statement about the physical system's state after the measurement according to the laws of quantum theory. However, in most of the interpretations of quantum theory, the resulting statements of the two observers contradict each other. This reflects a seeming incompatibility of two laws in quantum theory: the deterministic and continuous time evolution of the state of a closed system and the probabilistic, discontinuous collapse of the state of a system upon measurement. Wigner's friend is therefore directly linked to the measurement problem in quantum mechanics with its famous Schrödinger's cat paradox. The thought experiment posits a friend of Wigner in a laboratory, and lets the friend perform a quantum measurement on a physical system (this could be a spin system or something analogous to Schrödinger's cat). This system is assumed to be in a superposition of two distinct states, say, state 0 and state 1 (or 'dead' and 'alive', in the case of Schrödinger's cat). When Wigner's friend measures the system in the 0/1-basis, according to quantum mechanics, they will get one of the two possible outcomes (0 or 1) and the system collapses into the corresponding state.