4 ms·

Why is information loss such a big deal? Information gets lost all the time. Hit the wrong button, and the all-important file vault is gone, with all the backup

Why is information loss such a big deal? Information gets lost all the time. Hit the wrong button, and the all-important file vault is gone, with all the backups, forever, information in them is lost. You might lose a job, but the universe doesn't break because of that!

tsimionescu 5y ago
Not sure if you are joking, but the article covers this. In principle, according to QM, information is never lost (until you make a measurement, but that's a different can of worms). In principle, in QM it is impossible to delete information. The article explains: if you burn a book, but gather detailed information about the fire and the smoke, you can reconstruct exactly what every letter on every page looked like, and every ink blot you spilled on it 10 years ago.
- xaedes 5y ago
  Burn it to ash, collect info about the ash and reconstruct - no problem. But if you burn it in a way, that the only remains are "random thermal radiation" all the information is lost and we have a serious paradox to resolve...
  - tsimionescu 5y ago
    > But if you burn it in a way, that the only remains are "random thermal radiation" all the information is lost and we have a serious paradox to resolve... To quote the famous Spartan answer, If. That is, QM predicts this is impossible. Even if you threw the book into the Sun, you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book.
    - kgwgk 5y ago
      > according to QM, information is never lost (until you make a measurement > you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book Does the “information” [1] survive measurements or not? [1] “Information? Whose information? Information about what?”
      - tsimionescu 5y ago
        > Does the “information” [1] survive measurements or not? My understanding is that it doesn't, but I believe that may depend on your interpretation of QM. Note also that "measurement" is pretty ill-defined. > “Information? Whose information? Information about what?” About the state of the system (the wavefunction). Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was. Maybe the problem is more clear if moving to computation from pure physics: In a classical computer, you can do something like "x = x & y; y = y & x". If you run this operation and find that x = 0 and y = 0, you can't know what values x and y had before, so that information was lost (ignoring other physical effects - if QM is right, the information is still retained, maybe radiated away by the processor or something). As such, in a quantum computer, this operation simply can't be performed. Instead, you have to use an ancillary bit, z, and some QC equivalent of the Toffoli gate [0]. Then you can compute something like {x, y, z} = {x, y, z XOR (x AND y)}; {y, x, z} = {y, x, z XOR (y AND x)}; if you get the result {0, 0, 1}, you can compute exactly what values x, y and z had initially. The same observations apply to physical interactions. [0] https://en.wikipedia.org/wiki/Toffoli_gate https://en.wikipedia.org/wiki/Toffoli_gate
        kgwgk 5y ago
        Then you don’t think that it’s necessarily possible - even in principle - to identify the words in the book that you threw the into the Sun _measuring_ the radiation? > Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was. There is no way to know in what state is an isolated system - unless you know the state when you last interacted with it. You can “set” the state now and deduce the future evolution. You cannot “know” the state now and deduce the past evolution. If you think about the whole universe, the “state” that could be described by a “wavefunction” is not a state describing the observed universe. Not even the number of elementary particles would be defined. The physical relevance is unclear.
        5y ago
- Andrew_nenakhov 5y ago
  Or the QM is just wrong about information never being lost.
  - tsimionescu 5y ago
    Sure, that's a possibility. But, the problem is that this feature comes from a very fundamental place in QM's mathematics - QM is (almost) a linear theory, and with linear equations, information can't be lost. So, to assert that QM is wrong about this is to invalidate all of QM's equations. Now, it's important to recognize one thing: QM is not really a linear theory, because it also has Born's rule, or the Measurement postulate. That is, while the wavefunction evolves according to purely linear equations, when you ultimately want to measure the state of the system, you get a non-linear update: the wavefunction suddenly "collapses" to a single value, and information is indeed lost (different wave-functions can collapse to the same state after a measurement). However, the measurement postulate is itself poorly understood, so its hard to introduce it into the discussion without derailing things. There are even consistent interpretations of QM where this doesn't actually happen, such as Many Worlds, where the information is actually still preserved across the totality of the worlds.
    - kgwgk 5y ago
      > the information is actually still preserved across the totality of the worlds That may be correct if the “totality of the worlds” means one single “world” described by a wave function evolving unitarily - corresponding to what you call information. This “information” cannot be destroyed but it cannot be created either. It will always be the same “information” that was already there at the beginning of time. What is unclear is the “many worlds” part. How are they defined?
      - tsimionescu 5y ago
        > It will always be the same “information” that was already there at the beginning of time. Yes, absolutely. Though it's worth noting that QM does allow for the void to have random fluctuations that are not caused by anything else, but that can interact with the existing system. > What is unclear is the “many worlds” part. How are they defined? There are several ways from what I've read. I personally don't think MWI really solves any problems, or that it is a good description of nature, so I haven't taken too much time to remember exactly how they do it.

tsimionescu 5y ago

Not sure if you are joking, but the article covers this. In principle, according to QM, information is never lost (until you make a measurement, but that's a different can of worms). In principle, in QM it is impossible to delete information. The article explains: if you burn a book, but gather detailed information about the fire and the smoke, you can reconstruct exactly what every letter on every page looked like, and every ink blot you spilled on it 10 years ago.

xaedes 5y ago
Burn it to ash, collect info about the ash and reconstruct - no problem. But if you burn it in a way, that the only remains are "random thermal radiation" all the information is lost and we have a serious paradox to resolve...
- tsimionescu 5y ago
  > But if you burn it in a way, that the only remains are "random thermal radiation" all the information is lost and we have a serious paradox to resolve... To quote the famous Spartan answer, If. That is, QM predicts this is impossible. Even if you threw the book into the Sun, you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book.
  - kgwgk 5y ago
    > according to QM, information is never lost (until you make a measurement > you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book Does the “information” [1] survive measurements or not? [1] “Information? Whose information? Information about what?”
    - tsimionescu 5y ago
      > Does the “information” [1] survive measurements or not? My understanding is that it doesn't, but I believe that may depend on your interpretation of QM. Note also that "measurement" is pretty ill-defined. > “Information? Whose information? Information about what?” About the state of the system (the wavefunction). Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was. Maybe the problem is more clear if moving to computation from pure physics: In a classical computer, you can do something like "x = x & y; y = y & x". If you run this operation and find that x = 0 and y = 0, you can't know what values x and y had before, so that information was lost (ignoring other physical effects - if QM is right, the information is still retained, maybe radiated away by the processor or something). As such, in a quantum computer, this operation simply can't be performed. Instead, you have to use an ancillary bit, z, and some QC equivalent of the Toffoli gate [0]. Then you can compute something like {x, y, z} = {x, y, z XOR (x AND y)}; {y, x, z} = {y, x, z XOR (y AND x)}; if you get the result {0, 0, 1}, you can compute exactly what values x, y and z had initially. The same observations apply to physical interactions. [0] https://en.wikipedia.org/wiki/Toffoli_gate https://en.wikipedia.org/wiki/Toffoli_gate
      - kgwgk 5y ago
        Then you don’t think that it’s necessarily possible - even in principle - to identify the words in the book that you threw the into the Sun _measuring_ the radiation? > Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was. There is no way to know in what state is an isolated system - unless you know the state when you last interacted with it. You can “set” the state now and deduce the future evolution. You cannot “know” the state now and deduce the past evolution. If you think about the whole universe, the “state” that could be described by a “wavefunction” is not a state describing the observed universe. Not even the number of elementary particles would be defined. The physical relevance is unclear.
        5y ago
Andrew_nenakhov 5y ago
Or the QM is just wrong about information never being lost.
- tsimionescu 5y ago
  Sure, that's a possibility. But, the problem is that this feature comes from a very fundamental place in QM's mathematics - QM is (almost) a linear theory, and with linear equations, information can't be lost. So, to assert that QM is wrong about this is to invalidate all of QM's equations. Now, it's important to recognize one thing: QM is not really a linear theory, because it also has Born's rule, or the Measurement postulate. That is, while the wavefunction evolves according to purely linear equations, when you ultimately want to measure the state of the system, you get a non-linear update: the wavefunction suddenly "collapses" to a single value, and information is indeed lost (different wave-functions can collapse to the same state after a measurement). However, the measurement postulate is itself poorly understood, so its hard to introduce it into the discussion without derailing things. There are even consistent interpretations of QM where this doesn't actually happen, such as Many Worlds, where the information is actually still preserved across the totality of the worlds.
  - kgwgk 5y ago
    > the information is actually still preserved across the totality of the worlds That may be correct if the “totality of the worlds” means one single “world” described by a wave function evolving unitarily - corresponding to what you call information. This “information” cannot be destroyed but it cannot be created either. It will always be the same “information” that was already there at the beginning of time. What is unclear is the “many worlds” part. How are they defined?
    - tsimionescu 5y ago
      > It will always be the same “information” that was already there at the beginning of time. Yes, absolutely. Though it's worth noting that QM does allow for the void to have random fluctuations that are not caused by anything else, but that can interact with the existing system. > What is unclear is the “many worlds” part. How are they defined? There are several ways from what I've read. I personally don't think MWI really solves any problems, or that it is a good description of nature, so I haven't taken too much time to remember exactly how they do it.