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Why It Is Wrong To Say That Qubits Are "0 And 1 At The Same Time"
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​​​​​​​​​​​​​​In this post, I will explain why interpreting a qubit as a quantum system that is both 0 and 1 at the same time is incorrect.
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I understand that this is an attempt to convey a difficult concept (quantum superposition) in simple terms.
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However, this description is misleading and perpetuates a misconception about the quantum world: that it is a superposition of classical worlds.
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This misunderstanding leads to inaccurate statements in quantum computing, such as "a quantum computer tries all possible solutions at once and chooses the correct one."
On a grander scale, some people claim "there are infinite universes at the same time."
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Superposition of Motion in Classical Mechanics
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Consider a projectile launched at an angle between zero and ninety degrees with respect to the ground.
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In his "Dialogue Concerning Two New Sciences," Galileo explained that the motion of the projectile can be described as two independent motions: horizontal and vertical.
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Using a Cartesian coordinate system with the x-axis along the ground level and the y-axis vertical, the position of the projectile over time can be expressed as functions of these coordinates.
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The projectile's position is given in terms of time, so the horizontal and vertical motions are also functions of time.
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It is natural to say that the particle moves "at the same time," or "simultaneously," in the x and y directions.
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In modern vector notation, the position vector at any time t is given by:
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V(t) = [ v_x(t) v_y(t) ]^T
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This isn’t how things work in the quantum world.
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Two Quantum States at Once
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Richard Feynman believed that the double-slit experiment "has in it the heart of quantum mechanics."
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This experiment, also discussed by David Bohm and John Bell to explore the core ideas of quantum mechanics, was popularized by Feynman in his Lectures on Physics.
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It has become a foundational thought experiment for introducing quantum concepts to the general public.
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It is used by everyone attempting to explain quantum superposition, from enthusiasts to experts.
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I suppose that you are familiar with it.
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Pay close attention, as the following argument is fundamentally flawed.
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It is claimed that, since photons behave according to quantum mechanics and produce an interference pattern on the screen, the only possible logical conclusion is that they pass through both slits simultaneously.
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It is thus natural to mathematically describe their state as a superposition of both possibilities, ∣u⟩ and ∣l⟩:
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∣ψ⟩=½ ∣u⟩+½ ∣l⟩ .
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If the probabilities of passing through the slits are not equal, maybe because one slit is slightly bigger than the other, this is generalized to
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∣ψ⟩=α_u ∣u⟩+α_l ∣l⟩ ,
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where ∣α_u∣^2 and ∣α_l∣^2 represent the probabilities of passing through the upper and lower slits, respectively.
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Photons are, thus, described as being in a superposition of states, namely, passing through both slits simultaneously.
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This mathematical framework also applies to other quantum two-level systems, such as qubits.
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If a classical bit represents a state of information with values b=0 or b=1, a qubit is a quantum system that exists in a superposition of both states simultaneously, ∣0⟩ and ∣1⟩,
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∣q⟩=α_0∣0⟩+α_1∣1⟩ .
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More complex systems, such as Schrödinger's cat, can also be described using this principle.
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Before opening the box, Schrödinger's cat exists in the state:
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∣cat⟩=α_a ∣a⟩+α_d ∣d⟩ ,
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where ∣a⟩ and ∣d⟩ represent the "alive" and "dead" states, respectively.
Similar to the motion of a projectile, the states of photons, qubits and cats are described as simultaneously occupying two incompatible states.
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The only thing that is correct in this argument is the math.
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The physical interpretation is incorrect—at least from the point of view of quantum mechanics!
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What Quantum Mechanics Really Tells Us
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There is almost no physicist or quantum computing expert who, when talking to non-experts, does not introduce a qubit by saying that it is a quantum system in two classical states, 0 and 1, at the same time.
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Previously, I have explained the classical origin of this misinterpretation.
Let me now explain how physicists are introduced to two-level quantum systems.
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The approach is historical and within the context of quantum physics.
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We learn that two German physicists, Otto Stern and Walther Gerlach, studied the behavior of narrow beams of silver atoms passing through non-uniform magnetic fields.
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They discovered that, regardless of the magnet's orientation, the spots on the screen indicated that the beam split into two distinct parts (instead of a continuous beam ranging from maximum to no deflection).
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They concluded that this was due to the intrinsic magnetic moment (the spin) of the single electron in the silver atoms, which had two opposite discrete values, say + and -.
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Associated with these values are two vectors, denoted |+⟩ and |-⟩, respectively.
Mathematically, the state of the electron before measurement is described by the vector:
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|e⟩ = a |+⟩ + b |-⟩ ,
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where a and b, the so-called probability amplitudes, are complex numbers.
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These quantum numbers are not arbitrary; they must satisfy the experimental results.
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The fact that a and b are complex numbers is the crucial difference between quantum and classical two-level systems.
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As quantum numbers, they can be written as complex exponentials, and the phase difference between them plays a crucial role in the system's "coherence".
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Something that does not occur in classical physics.
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For example, this explains the interference pattern of electrons and photons in the double-slit experiment.
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Notice that there is no mention of time, let alone "in two states at the same time" or "simultaneously."
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The description is purely mathematical!
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Just like in linear algebra, when we say that a vector A is the sum of vectors B and C, we do not say that A is simultaneously B and C.
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The same holds for quantum mechanics.
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The description is purely mathematical!
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We are taught that quantum mechanics only tells us about the measurement probabilities, not about what happens between the preparation of the quantum system and the measurement.
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There are some things in the quantum mechanical way of describing the world that are simply "unspeakable", as John Bell put it.
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This is what is amazing about quantum mechanics, not that the qubit is 0 and 1 at the same time or that the electron passes through both slits in the double-slit experiment.
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If you do not accept this, you will not be able to understand the true nature of paradoxes like Schrödinger's cat and Einstein's "spooky action at a distance".
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Want to dive deeper? My eBook is a great place to start → https://www.ozatp.com/qaf
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