“Feveral kinds of hairy mouldy fpots”

The book had a sheepskin cover, and mold was growing on the sheepskin. Robert Hooke, a pioneering microbiologist, slid the cover under one of the world’s first microscopes. Mold, he discovered, consists of “nothing elfe but feveral kinds of fmall and varioufly figur’d Mufhroms.” He described the Mufhroms in his treatise Micrographia, a 1665 copy of which I found in “Beautiful Science.” An exhibition at San Marino’s Huntington Library, “Beautiful Science” showcases the physics of rainbows, the stars that enthralled Galileo, and the world visible through microscopes.

Hooke image copy

Beautiful science of yesterday: An illustration, from Hooke’s Micrographia, of the mold.

[T]hrough a good Microfcope,” Hooke wrote, the sheepskin’s spots appeared “to be a very pretty fhap’d Vegetative body.”

How like a scientist, to think mold pretty. How like quantum noise, I thought, Hooke’s mold sounds.

Quantum noise hampers systems that transmit and detect light. To phone a friend or send an email—“Happy birthday, Sarah!” or “Quantum Frontiers has released an article”—we encode our message in light. The light traverses a fiber, buried in the ground, then hits a detector. The detector channels the light’s energy into a current, a stream of electrons that flows down a wire. The variations in the current’s strength is translated into Sarah’s birthday wish.

If noise doesn’t corrupt the signal. From encoding “Happy birthday,” the light and electrons might come to encode “Hsappi birthdeay.” Quantum noise arises because light consists of packets of energy, called “photons.” The sender can’t control how many photons hit the detector.

To send the letter H, we send about 108 photons.* Imagine sending fifty H’s. When we send the first, our signal might contain 108– 153 photons; when we send the second, 108 + 2,083; when we send the third, 108 – 6; and so on. Receiving different numbers of photons, the detector generates different amounts of current. Different amounts of current can translate into different symbols. From H, our message can morph into G.

This spring, I studied quantum noise under the guidance of IQIM faculty member Kerry Vahala. I learned to model quantum noise, to quantify it, when to worry about it, and when not. From quantum noise, we branched into Johnson noise (caused by interactions between the wire and its hot environment); amplified-spontaneous-emission, or ASE, noise (caused by photons belched by ions in the fiber); beat noise (ASE noise breeds with the light we sent, spawning new noise); and excess noise (the “miscellaneous” folder in the filing cabinet of noise types).

Vahala image copy

Beautiful science of today: A microreso-nator—a tiny pendulum-like device— studied by the Vahala group.

Noise, I learned, has structure. It exhibits patterns. It has personalities. I relished studying those patterns as I relish sending birthday greetings while battling noise. Noise types, I see as a string of pearls unearthed in a junkyard. I see them as “pretty fhap[es]” in Hooke’s treatise. I see them—to pay a greater compliment—as “hairy mouldy fpots.”


*Optical-communications ballpark estimates:

  • Optical power: 1 mW = 10-3 J/s
  • Photon frequency: 200 THz = 2 × 1014 Hz
  • Photon energy: h???? = (6.626 × 10-34 J . s)(2 × 1014 Hz) = 10-19 J
  • Bit rate: 1 GB = 109 bits/s
  • Number of bits per H: 10
  • Number of photons per H: (1 photon / 10-19 J) (10-3 J/s)(1 s / 109 bits)(10 bits / 1 H) = 108


An excerpt from this post was published today on Verso, the blog of the Huntington Library, Art Collection, and Botanical Gardens.

With thanks to Bassam Helou, Dan Lewis, Matt Stevens, and Kerry Vahala for feedback. With thanks to the Huntington Library (including Catherine Wehrey) and the Vahala group for the Micrographia image and the microresonator image, respectively.


  1. […] further details about noise, see the full version of this article on Caltech’s “Quantum Frontiers” blog. With thanks to Bassam Helou, Dan Lewis, Matt Stevens, and Kerry Vahala for feedback. With thanks […]

  2. James Dwyer June 12, 2014 at 10:53 am - Reply

    Interesting post, but out communication of information is not actually so haphazard as the illustrated calculation of the potential for raw optical fiber signal errors implies.

    I’m certainly no communications expert, but in general terms we send digitally encoded binary data, so that each text character is represented by 7 or 8 bits with a parity bit used for error detection of each character. However, characters are transmitted in blocks that are additionally encoded with error correction information so that some transmission errors can be corrected, and hopefully all that cannot can be detected. Blocks with errors are not accepted by the receiver: they are subsequently retransmitted until they are received without error. Control software monitors the frequency of erroneous transmissions for each link – indicating when retransmission frequencies are effecting link performance… There’s a lot going on ‘under the covers’ to ensure the error-free remote transmission of information.

    BTW, I think that it’s most likely that a message signal containing fifty consecutive H’s would be compressed into some short form somewhat like “>c50-H<"…

    • Nicole Yunger Halpern June 12, 2014 at 11:30 am - Reply

      James, thanks for pointing out the subtleties. I agree, I omitted many details, and the calculations are ballpark. The goal was to convey approximately what quantum noise is. Doing what physicists often do, I simplified the problem to emphasize key ideas, and I used back-of-the-envelope calculations. Of course, different people might have different opinions about which ideas are key. I was grateful to have been able to run the approach by researchers who have more electrical-engineering and telecom experience than I. I encourage any interested readers to Google the tools you mentioned.

      I agree about representing natural-language letters in terms of bits, which is why the calculation includes a bit rate. I agree that hardly anyone would want to send fifty Hs individually. For starters, good luck sending a meaningful message in fifty Hs! Again, the goal was to illustrate one key idea: The number of photons used to transmit some message varies from copy of that message to copy. This variation amounts to noise.

  3. John Sidles June 13, 2014 at 4:57 am - Reply

    Nicole Yunger Halpern writes  “Light traverses a fiber, buried in the ground, then hits a detector. The detector channels the light’s energy into a current, a stream of electrons that flows down a wire.”

    This Great Truth’s dual-view is wonderful too:

    Nicole’s Dual View  “A stream of electrons flowing through a detector injects vacuum into an optical fiber, whose fluctuations modulate photon source-currents so as to agree with the detector-current fluctuations.”

    Here Carlton Caves’ advice applies: “Physicists are really obliged to give every explanation they can think of.” This applies particularly to the entangling interactions of quantum symplectic flows (i.e., Hamiltonian dynamical processes) with quantum metric flows (i.e., Lindbladian measurement processes).

    Embracing both of these dual-views helps us to appreciate why (for example) scalable quantum computers and scalable BosonSampling experiments have proven to be so terrifically fun to conceive, and yet so terribly challenging to design and operate.

    Caves’ advice appears in a outstanding interview (as it seems to me) titled “Realizing Squeezing: An interview with Carlton Caves” (which a Google search finds).

    @article{Author = {Michael Landry},Journal = {LIGO Magazine},Month = {September},Number = {3},Pages = {page 16-19},Title = {Realizing Squeezing: An interview with Carlton Caves},Volume = {1},Year = {2013}}
  4. ychen June 13, 2014 at 9:27 am - Reply

    Very interesting asticle (with quantum noise) 😀 ! Regarding “Noise types, I see as a string of pearls unearthed in a junkyard”, do you have any good example how noise, or noise type can be a useful tool, rather than something that hampers or damages our quantum system? Thank you 😀

  5. juven June 13, 2014 at 8:56 pm - Reply

    I recall a letter adopted in the prelude in a chapter (on Supersymmetry of Ryder QFT book):

    “This morning I visited the place where the street-cleaners dump the rubbish. Oh… My God… it was beautiful.” – Van Gogh

    • Nicole Yunger Halpern June 14, 2014 at 10:07 pm - Reply


  6. B August 24, 2014 at 9:50 pm - Reply

    I think the f in your quotes of Hooke is actually a long s in type.

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