Quantum superposition is really weird because it is fundamentally different than "either definite state but I don't know which", because the superposition state leads to different measurements than the non-superposition state.
Examples:
- www.youtube.com/watch?v=tt8gVXDsh7Q "Interference in quantum mechanics" by Looking Glass Universe (2015) shows how a left-right spin measurement has a defined value for a superposed half up half down state, but not for a pure up state.TODO can this be conducted? As mentioned in the video, this is closely linked to the fact that you can describe the wave function in multiple different bases (up/down or left/right), which is also at the root of the uncertainty principle.
- Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)" gives a similar photon version
- it seems that the single particle double slit experiment can also be thought of as in terms of a superposition of "the particle goes through the right" and "the particle goes through the right", although it is a bit harder to thing about as it is not a discrete process
Future self, answer these.
20 years
- 2018-2038: are companies offering free full genome decoding just to get your genomic data and sell it to pharma companies?Someone like Ciro then creates an open source genomic database funded by health organizations that publishes genomes + phenotypes anonymously. Genome to phenotype analytics go crazy big.
40 years:
- 2017-2057: was human level AI reached (by non-bio devices :-)), even if very slow?
- 2017-2057: did China become democratic?
- 2018-2058: did impressive brain-computer interfaces show up?
Here is a very direct description of the system:Code 1. "Sample Bitcoin transaction graph" illustrates these concepts:
- each transaction (transaction is often abbreviated "tx") has a list of inputs, and a list of outputs
- each input is the output of a previous transaction. You verify your identity as the indented receiver by producing a digital signature for the public key specified on the output
- each output specifies the public key of the receiver and the value being sent
- the sum of output values cannot obvious exceed the sum of input values. If it is any less, the leftover is sent to the miner of the transaction as a transaction fee, which is an incentive for mining.
- once an output is used from an input, it becomes marked as spent, and cannot be reused again. Every input uses the selected output fully. Therefore, if you want to use an input of 1 BTC to pay 0.1 BTC, what you do is to send 0.1 BTC to the receiver, and 0.9 BTC back to yourself as change. This is why the vast majority of transactions has two outputs: one "real", and the other change back to self.
tx0: magic transaction without any inputs, i.e. either Genesis block or a coinbase mining reward. Since it is a magic transaction, it produces 3 Bitcoins from scratch: 1 inout0and 2 inout1. The initial value was actually 50 BTC and reduced with time: Section "Bitcoin halving"tx1: regular transaction that takes:Since this is a regular transaction, no new coins are produced.tx2: regular transaction with a single input and a single output. It uses up the entire input, leading to 0 miner fees, so this greedy one might (will?) never get mined.tx3: regular transaction with two inputs and one output. The total input is 2.3, and the output is 1.8, so the miner fee will be 0.5
tx1 tx3
tx0 +---------------+ +---------------+
+----------+ | in0 | | in0 |
| out0 |<------out: tx0 out0 | +------out: tx1 out1 |
| value: 1 | +---------------+ | +---------------+
+----------+ | out0 | | | in1 |
| out1 |<-+ | value: 0.5 | | +----out: tx2 out0 |
| value: 2 | | +---------------+ | | +---------------+
+----------+ | | out1 |<-+ | | out1 |
| | value: 0.3 | | | value: 1.8 |
| +---------------+ | +---------------+
| |
| |
| |
| tx2 |
| +---------------+ |
| | in0 | |
+----out: tx0 out1 | |
+---------------+ |
| out0 |<---+
| value: 2 |
+---------------+Code 1.
Sample Bitcoin transaction graph
. Since every input must come from a previous output, there must be some magic way of generating new coins from scratch to bootstrap the system. This mechanism is that when the miner mines successfully, they get a mining fee, which is a magic transaction without any valid inputs and a pre-agreed value, and an incentive to use their power/compute resources to mine. This magic transaction is called a "coinbase transaction".
The key innovation of Bitcoin is how to prevent double spending, i.e. use a single output as the input of two different transactions, via mining.
For example, what prevents me from very quickly using a single output to pay two different people in quick succession?
The solution are the blocks. Blocks discretize transactions into chunks in a way that prevents double spending.
A block contains:
- a list of transactions that are valid amongst themselves. Notably, there can't be double spending within a block.People making transactions send them to the network, and miners select which ones they want to add to their block. Miners prefer to pick transactions that are:
- the ID of its parent block. Blocks therefore form a linear linked list of blocks, except for temporary ties that are soon resolved. The longest known list block is considered to be the valid one.
- a nonce, which is an integer chosen "arbitrarily by the miner"
For a block to be valid, besides not containing easy to check stuff like double spending, the miner must also select a nonce such that the hash of the block starts with N zeroes.
For example, considering the transactions from Code 1. "Sample Bitcoin transaction graph", the block structure shown at Code 2. "Sample Bitcoin blockchain" would be valid. In it
block0 contains two transactions: tx0 and tx1, and block1 also contains two transactions: tx2 and tx3. block0 block1 block2
+------------+ +--------------+ +--------------+
| prev: |<----prev: block0 |<----prev: block1 |
+------------+ +--------------+ +--------------+
| txs: | | txs: | | txs: |
| - tx0 | | - tx2 | | - tx4 |
| - tx1 | | - tx3 | | - tx5 |
+------------+ +--------------+ +--------------+
| nonce: 944 | | nonce: 832 | | nonce: 734 |
+------------+ +--------------+ +--------------+
Code 2.
Sample Bitcoin blockchain
. nonces are on this example arbitrary chosen numbers that would lead to a desired hash for the block.block0 is the Genesis block, which is magic and does not have a previous block, because we have to start from somewhere. The network is hardcoded to accept that as a valid starting point.Now suppose that the person who created Clearly, this transaction would try to spend Notably, it is not possible that
tx2 had tried to double spend and also created another transaction tx2' at the same time that looks like this: tx2'
+---------------+
| in0 |
| out: tx0 out1 |
+---------------+
| out0 |
| value: 2 |
+---------------+tx0 out1 one more time in addition to tx2, and should not be allowed! If this were attempted, only the following outcomes are possible:block1containstx2. Then whenblock2gets made, it cannot containtx2', becausetx0 out1was already spent bytx2block1containstx2'.tx2cannot be spent anymore
block1 contains both tx2 and tx2', as that would make the block invalid, and the network would not accept that block even if a miner found a nonce.Since hashes are basically random, miners just have to try a bunch of nonces randomly until they find one that works.
The more zeroes, the harder it is to find the hash. For example, on the extreme case where N is all the bits of the hash output, we are trying to find a hash of exactly 0, which is statistically impossible. But if e.g. N=1, you will in average have to try only two nonces, N=2 four nonces, and so on.
The value N is updated every 2 weeks, and aims to make blocks to take 10 minutes to mine on average. N has to be increased with time, as more advanced hashing hardware has become available.
Once a miner finds a nonce that works, they send their block to the network. Other miners then verify the block, and once they do, they are highly incentivized to stop their hashing attempts, and make the new valid block be the new parent, and start over. This is because the length of the chain has already increased: they would need to mine two blocks instead of one if they didn't update to the newest block!
Therefore if you try to double spend, some random miner is going to select only one of your transactions and add it to the block.
They can't pick both, otherwise their block would be invalid, and other miners wouldn't accept is as the new longest one.
Then sooner or later, the transaction will be mined and added to the longest chain. At this point, the network will move to that newer header, and your second transaction will not be valid for any miner at all anymore, since it uses a spent output from the first one that went in. All miners will therefore drop that transaction, and it will never go in.
The goal of having this mandatory 10 minutes block interval is to make it very unlikely that two miners will mine at the exact same time, and therefore possibly each one mine one of the two double spending transactions. When ties to happen, miners randomly choose one of the valid blocks and work on top of it. The first one that does, now has a block of length L + 2 rather than L + 1, and therefore when that is propagated, everyone drops what they are doing and move to that new longest one.
Quantum version of the Hall effect.
As you increase the magnetic field, you can see the Hall resistance increase, but it does so in discrete steps.
Gotta understand this because the name sounds cool. Maybe also because it is used to define the fucking ampere in the 2019 redefinition of the SI base units.
At least the experiment description itself is easy to understand. The hard part is the physical theory behind.
The effect can be separated into two modes:
- Integer quantum Hall effect: easier to explain from first principles
- Fractional quantum Hall effect: harder to explain from first principles
- Fractional quantum Hall effect for : 1998 Nobel Prize in Physics
- Fractional quantum Hall effect for : one of the most important unsolved physics problems as of 2023
We get the time-independent Schrödinger equation by substituting this into Equation "time-independent Schrödinger equation for a one dimensional particle":
Now, there are two ways to go about this.
The first is the stupid "here's a guess" + "hey this family of solutions forms a complete basis"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.
The second is the much celebrated ladder operator method.
Man-in-the-middle attack
quantumcomputing.stackexchange.com/questions/142/advantage-of-quantum-key-distribution-over-post-quantum-cryptography/25727#25727 Advantage of quantum key distribution over post-quantum cryptography has Ciro Santilli's comparison to classical encryption.
Long story short:
- QKD allows you to generate shared keys without public-key cryptography. You can then use thses shared keys
- QKD requires authentication on a classical channel, exactly like a classical public-key cryptography forward secrecy would. The simplest way to do this is a with a pre-shared key, just like in classical public key cryptography. If that key is compromised at any point, your future messages can get man-in-the-middle'd, exactly like in classical cryptography.
QKD uses quantum mechanics stuff to allow sharing unsnoopable keys: you can detect any snooping and abort communication. Unsnoopability is guaranteed by the known laws of physics, up only to engineering imperfections.
Furthermore, it allows this key distribution without having to physically take a box by car somewhere: once the channel is established, e.g. optical fiber, you can just keep generating perfect keys from it. Otherwise it would be pointless, as you could just drive your one-time pad key every time.
However, the keys likely have a limited rate of generation, so you can't just one-time pad the entire message, except for small text messages. What you would then do is to use the shared key with symmetric encryption.
Therefore, this setup usually ultimately relies on the idea that we believe that symmetric encryption is safer than , even though there aren't mathematical safety proofs of either as of 2020.
Quantum matter physics course of the University of Oxford Updated 2025-05-21 +Created 1970-01-01
2011- professor: Steven H. Simon. His start date is given e.g. at: www-thphys.physics.ox.ac.uk/people/SteveSimon/condmat2012/LectureNotes2012.pdf which is presumably an older version of: www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2022/QuantumMatter.pdf
Notes/book: www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2022/QuantumMatter.pdf Marked as being for Oxford MMathPhys, so it appears that this is a 4th year course normally. TODO but where is it listed under the course list of MMapthPhys? mmathphys.physics.ox.ac.uk/course-schedule
Course page index: www-thphys.physics.ox.ac.uk/people/SteveSimon/
www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2023/quantummatter.html mentions it is given in Hilary term
2023 syllabus as per www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2023/quantummatter.html#Syllabus:
- Fermi Liquids
- Weakly Interacting Fermions
- Response Functions and Screening
- Thomas Fermi
- RPA
- Plasmons
- Landau Fermi Liquid Theory
- Superfluidity
- Two Fluid Model and Quantized Circulation
- Landau Criterion for Superfluidity
- Two Fluid Model for Superconductors
- London Theory
- Flux Vortices
- Type I and Type II superconductors
- Microscopic Superfluidity
- Coherent States
- Bose Condensation
- Gross Pitaevskii Equation
- Off Diagonal Long Range Order
- Feynman Theory of Superfluidity (in book, but will skip in lectures. Not examinable)
- Ginzburg Landau Theory of Superfluids
- BCS Theory of Superconductors
There are unlisted articles, also show them or only show them.