Thursday, November 28, 2019

Quantum Ansible

Nikolai Nikitin and Konstantin Toms

A few days ago a paper appeared in the physics arXiv that described a clever new faster-than-light signaling scheme. The authors are a pair of Russians from the Lomonosov State University in Moscow, Nikolai Nikitin and Konstantin Toms, who is currently a postdoc at the University of New Mexico after spending time at the ATLAS experiment at CERN. N&T called their paper "Quantum Ansible" after a fictional FTL signaling device in the novels of Ursula LeGuin.

N&T's Quantum Ansible is a more sophisticated realization of my early (1982) FLASH FTL signaling scheme which imagined a universal quantum copying device that could exactly duplicate any unknown quantum state. My FLASH proposal was quickly refuted by Wootters, Zurek and others and led to the discovery/invention of the quantum no-cloning rule which plays an important part in the field of quantum computing.

Any classical datum can be easily copied, as simple as pushing the "Duplicate" command in your computer menu. But Nature outlaws such a duplicate command for quantum data. The best you can do, given an unknown quantum state, as was shown by Leonard Mandel, is to duplicate that state with 5/6 (= 83.3%) accuracy. As noise-free as this might seem, this small degree of copying imperfection was precisely sufficient to render my FLASH FTL communication scheme kaput.

The field of quantum computing has developed immensely since the discovery of the no-cloning rule. We know, for instance, that it is possible to perfectly clone any known quantum state. And thanks to the field of quantum computing, there is an easy way to do so: the so-called CNOT gate (or Feynman gate, as it is sometimes called).

The four possible operations of the CNOT gate.

The CNOT gate has two inputs and two outputs. The top input traverses the gate unchanged; the bottom input flips its sign if the top input is |1>. If the top input is |0>, the bottom output remains the same. CNOT stands for "Controlled NOT": the top input controls whether the bottom input will remain the same or will be subjected to the NOT operation, which changes a one to a zero.

As simple as this gate seems to be, the CNOT gate plays an important role in quantum computing. It can, for instance, be used to clone a known quantum state, without the use of lasers.

In a classical computer the inputs and outputs of the CNOT gate are simple binary bits, symbolized by zeros and ones. In a quantum computer, the inputs and outputs are quantum states, symbolized (in Dirac notation) by |0>s and |1>s. In the case of the quantum ansible, |0> represents the spin-down state of Alice's electron in the z-direction, a quantum state which could also be symbolized as:

|0> ----> | minus z--Alice>

|1> ----> |plus z -- Alice>

With this re-interpretation of the operation of the CNOT gate, it is easy to see how this simple gate can be used as a cloning tool for an orthogonal pair of quantum states.

We consider only the gate operations labeled A and B. In these two cases the bottom input is always |0> which in the physical situation represents Alice's electron having spin down in the z direction). In these two special cases, we note that the CNOT gate will clone either the |0> or the |1> state if it is presented to the upper input. Simply put in a |0> and two |0>s come out. Put in a |1> and two |1>s come out. In this special situation the CNOT gate can be used as a simple cloning tool for one particular known quantum state.

The importance of cloning in faster-than-light signaling schemes cannot be overestimated. In the usual measurement situation you get just one chance to measure the spin state of a single photon or electron. With a cloning device you can get two or more chances to measure different physical properties of a single quantum entity.

The designers of the quantum ansible imagine Bob located 4 light-years away on Alpha Centauri sending a spin-entangled sequence of electrons to Alice on Earth. Bob measures one electron spin and sends the other partner of the pair to Alice. If Bob measures spin along the z axis, Alice's distant electron will immediately (!) acquire a z-direction spin (either up or down); if Bob measures along the x axis Alice's distant electron will instantly acquire an x-axis spin.

If Alice can detect the difference between a random sequence of z-polarized electrons and a random sequence of x-polarized photons at her detector on Earth, then she can decode Bob's message (sent faster than light) which is encoded by his conscious decision at Alpha Centauri to switch his electron spin detector between the z-direction and the x-direction.

Given this situation, Nikitin & Toms make a clever move: they actually attempt to exploit the no-cloning rule in their favor. You can clone one known state (says Nature). So N&T choose to clone Alice's electron spin in the z-direction. But you are forbidden, says Nature, to clone any other spin direction.

That's fine, say Nikitin and Toms: we'll get great results measuring z-spin, because we can use a z-cloner. And we'll get terrible results when Bob sends x-polarized electrons. And from the difference between our good results and our terrible results, we'll be able to decode Bob's signal.

Ha. Ha, Nature. We Russians have finally fooled you.

Good results means an accurately measured z-spin of every electron. Terrible results mean a completely unpolarized beam of electrons with no directional preference whatsoever.


So far I have sketched the alleged operation of N&T's quantum ansible as it appears in their eight-page paper. Now I add my own comments.

This ansible scheme would actually work if everything behaved as they described it. But the weak point is N&T's assumption of a completely depolarized beam at Alice's site when Bob chooses to measure x-polarization. In a truly unpolarized beam, at the very least, Alice's cloner would refuse to work (because it's operating on an unknown state) and would not only produce two electrons of the same polarization all of the time but two electrons of different polarizations some of the time. The math (correct in my estimation) shows that this never happens. In fact, Alice's cloner continues to produce pairs of z-polarized photons, despite the alleged total polarization scrambling expected to occur due to Bob's choice to measure another polarization orthogonal to the direction that Alice's cloner is tuned to. In fact, from N&T's math alone, one can see that the physical situation at Alice's site seems to change when Bob decides to measure one spin direction rather than another, but the statistical outcome at Alice's site remains exactly the same.

Here's an analogy to what seems to be happening in the quantum ansible expeiment.

In my right-hand pocket I have a bunch of fake coins: either heads on both sides or tails on both sides. I pull one out and flip it. The result is known for sure. But I pick the coins at random from my pocket. The result is a random sequence of heads and tails. This physical situation (I claim) is analogous to Bob choosing to measure his electrons in the z-direction, the direction in which Alice happens to possess a perfect cloner.

In my left-hand pocket I have a bunch of fair coins: heads on one side, tails on the other. I pick a coin at random and flip it on the table. The result is a random sequence of heads and tails. This physical situation (I claim) is analogous to Bob choosing to measure his electrons in the x-directions, at a right angle to the direction in which Alice possesses a perfect cloner.

In both the coin analogy and the ansible experiment the actual physical situation seems to change depending on which pocket I select and which spin direction Bob selects (the math describing Alice's situation is certainly different for Bob's two choices). But although the physical situation seems to be different in both cases, the statistical predictions for the outcomes is exactly the same both for the coins and for Alice's measurements.

The quantum ansible is a gallant and clever attempt to exploit quantum entanglement to overcome Einstein's famous light-speed barrier to human information transfer. But despite its ingenuity, I do not believe it will work. Thank you, Nikitin and Toms, for an amusing physics puzzle.

At the conclusion of their quantum ansible paper, Nikolai Nikitin and Konstantin Toms thank a certain C. Aleister (Saint Genis-Pouilly, France) for creating a warm and friendly working atmosphere for discussion between the authors. With a bit of searching, I was able, on Facebook, to find a picture of these two Russian scientists' mysterious benefactor.

Aleister the cat illustrates the SO(3) rotation group