Schrodinger Cat

Schrödinger cat Review

A thought experiment proposed by Austrian physicist, Erwin Schrödinger, in 1935.

To illustrate the problem when Copenhagen interpretation is applied to macroscopic object.

Erwin Schrodinger do not accept the idea that the cat is both dead and alive simultaneously.

Erwin Schrodinger was so eager to know when will be the superposition state stop and turn into only one definite state out of all possible states.

Experiment Set-up

Copenhagen Interpretation

(Orthodox view)

Theory supporters are Neils Bohr, Werner Heisenberg etc.

There is no definite state of the system before measurement is made.

The states are in linear superposition state.

The act of measurement is collapsing the wave function to be in one of the definite state.

Non-deterministic interpretation (probabilistic)

Copenhagen interpretation (1)

Copenhagen interpretation (2)

|0> and |1> are two arbitrary states. Wavefunction will be collapsed into one of these states upon measurement is made and vice versa.

Born’s rule

It’s impossible to know the value of all the properties of the system at the same time. Heisenberg’s uncertainty principle

|ψ>¿α|0>+ β∨1>¿

Copenhagen interpretation on Schrödinger cat

After a certain of period of time, the poisonous radioactive atom is and the cat is before the box is open.

The wave function will be collapsed into only one of these states (alive or dead). Superposition state of wavefunction has collapsed.

The microscopic object can have linear superposition while macroscopic object cannot have ？？

Some doubts regardingCopenhagen interpretation

Why does measurement collapse the wavefunction ？

Measurement ‘creates’ the result ？

After collapse of wavefunction, what happen to the others unobservable states ？

What happen if there is a CCTV inside the sealed box, could the superposition state be observed ？

Many-World Interpretations

(MWI)

Many-World Interpretation (1)

Originally theorized by Hugh Everett in 1957, popularized and renamed by Bryce Seligman DeWitt in 1962.

There exists a relative phase information between the observer and the system (entanglement)

Each of states is physically real.

They are representing in their respective an universe.

Many World Interpretation (2)

The wavefunction collapsing in MWI is interpreted as the other states are evolving into a respectively split-branched universe.

At which, they are non-interactive with each other. Measurement caused the splitting.

They are sharing the same history before the measurement taken place.

They are evolving become different future but start from the same history background.

Many-world Interpretationon Schrödinger cat

The alive and dead cats are both equally real.

Observer is entangled with the cat’s state.

There is a phase information between the observer and the system.

Upon measurement, the cat is found at one definite state (alive or dead) in this universe.

While in the other universe, the cat is in opposite state with the state in previous universe.

Quantum Decoherence

(Phase-damping)

Phase-damping channel

Phase-damping channel is one type of quantum channel in quantum computation and information.

Channel to represent decoherence in actual quantum system.

Phase-damping channel

• Unitary representation of the phase-damping channel.

• p is the probability of environment scatter off from the qubit.

• The qubit remains unchanged.

Phase-damping channel

The three Kraus operator obtained from the unitary operator will take the form of:

Phase-damping channel

Hence, the operator sum representation is

Phase-damping channel

From the operator sum representation, the off diagonal term will decay away.

This is the reason why the cat was never observed in superposition state.