Quantum Entanglement David Badger Danah Albaum

Some thoughts on entanglement... “Spooky action at a distance.” -Albert Einstein “It is a problem that will drive you absolutely crazy.” -Pratim sen-Gupta, PhD student in physics “I don’t understand.” -David Badger, student in physics

A brief history of entanglement 1935: Einstein, Podolsky, and Rosen publish a paper attacking the Copenhagen interpretation of quantum mechanics The mathematics of QM allow for the violation of relativistic locality; the measurement of some quantity in one quantum system determines the same quantity in another quantum system, no matter how far away the two systems may be Einstein: Particles should have a definite state, independent of observation

1936: Schrodinger publishes an extension of the EPR paper, coining the term “entanglement” to describe the phenomenon Quantum states are NOT independent of observation; impossible to observe a quantum state without changing it Particles that are arbitrary distances apart can influence one another instantaneously

B How observation changes the state of a system We want to measure the spin on a neutron spin “up” spin “down” detector 1 detector 2 neutron A neutron has equal probability of being detected in either 1 or 2

B spin “up” spin “down” detector 1 detector 2 neutron wave function: ψ (s ↑) + ψ(s ↓) superposition of both spin states wave function: ψ (s ↑) * Ψ(deflected up) + ψ(s ↓) * Ψ(deflected down) the spin and position parts of the wave function have become entangled wave function: now, the detectors’ wave functions will become entangled with the neutron’s

So now we have a problem: What are the wave functions of the detectors? The detectors are macroscopic devices used to measure microscopic quantities Macroscopic measuring devices have an enormous number of quantum states We lose some information about the wave function of the neutron in the detector; this is called decoherence The only information we are left with are the relative probabilities that a detector will register

An illustration of non-locality We prepare two protons in a singlet state; one has spin up, the other has spin down along the y-axis ψ1 (s ↑ ) + ψ1 (s ↓) ψ2 (s ↑ ) + ψ2 (s ↓) proton 1 proton 2

An illustration of non-locality arbitrary distance proton 1proton 2 First we measure the spin of proton 1 along the y direction We will get ψ1 (s ↑ ) or ψ1 (s ↓) with equal prob. Let’s say we get ψ1 (s ↑ ) Our observation of system 1 changes the state of system 2. Then, the wave function of proton 2 instantaneously collapses to ψ2 (s ↓) and we will measure the spin to be “down”.

What does this mean? We “steered” wave function 2 into a certain form simply by making an observation about system 1 Neither of the protons was ever in a definite spin state, but both of them collapsed to one once we made an observation; the information about spin states is “encoded” in both of the protons Particles in an entangled system like this are called “qubits”, and are the theoretical basis for quantum computers

Quantum information and computing Superposition: a quantum system can take on two states at once Each qubit can encode both a 1 and a 0 at the same time The qubits are “linked” together through entanglement; measuring the state of one qubit affects the state of another

Quantum information and computing classical registerquantum register 3 bits encodes one symbol of eight combinations qubit register -> 8 3-bit symbols 1 3-bit register -> 1 3-bit symbol 3 qubits can encode all eight combinations at once 2^N symbols

Quantum information and computing The big problem: decoherence Decoherence increases with the number of quantum logic gates (qubits) Many physicists believe that decoherence will never be limited to an amount that allows more than a few quantum computations at once Research is going into decreasing decoherence by limiting the amount of macroscopic devices involved in the process

Recent advances in entanglement research Quantum cryptography: any eavesdropper changes the state of the system by observing it In 2004 physicists showed the transmission of a quantum cryptographic key over a 730 meter distance at 1 Mbps In 2003 three electrons were entangled using an ultrafast laser pulse and a magnetic quantum well. Previously, only two particles have been entangled at once in the laboratory Quantum synchronization of atomic clocks over long distances with unprecedented accuracy

Recent advances in entanglement research Entangled Quantum Interferometry: “dramatic noise reduction and sensitivity improvements in quantum measurements of tiny inertial motions” Quantum teleportation: destroying an unknown physical entity and recreating it in another location (a team at Innsbruck successfully recreated the polarization state of a photon across the room)

For more information Prof. Anton Zeilinger Introductions Qubits Stanford Encyclopedia of Philosophy Hidden Unity in Nature’s Laws by John C. Taylor