The 1935 Thought Experiment

Erwin Schrödinger introduced the cat in a paper titled “Die gegenwärtige Situation in der Quantenmechanik” (Naturwissenschaften, 1935). The paper is a critique of the Copenhagen interpretation of quantum mechanics, not an endorsement of macroscopic superposition.

The setup is familiar: a cat is placed in a sealed chamber with a radioactive atom, a Geiger counter, a hammer, and a vial of poison. If the atom decays in one hour, the counter fires, the hammer falls, the vial breaks, and the cat dies. If the atom does not decay, the cat lives. The atom is a quantum system; after one hour it is in a superposition of decayed and undecayed states.

Quantum mechanics — specifically, the Schrödinger equation, applied without any special rule for measurement — says the entire system (atom + counter + hammer + vial + cat) evolves into a superposition:

$$|\Psi\rangle = \frac{1}{\sqrt{2}}\bigl(|\text{decayed}\rangle|\text{cat dead}\rangle

• |\text{undecayed}\rangle|\text{cat alive}\rangle\bigr).$$

Schrödinger’s point was that this is absurd: the cat is either dead or alive, not a superposition of both, and any interpretation of quantum mechanics that predicts otherwise is failing at the level of macroscopic physical reality. He intended the cat as a reductio ad absurdum — a demonstration that taking the wave function literally at macroscopic scales leads to nonsense.

He was not proposing that cats are literally in superposition. He was proposing that the theory was incomplete.

What Actually Resolves the Cat

The resolution that modern physics offers is decoherence — the process by which a quantum superposition is destroyed through entanglement with the environment.

A macroscopic object — a cat, a hammer, a Geiger counter — is coupled to an enormous number of environmental degrees of freedom: air molecules, photons, phonons in its own structure. Each of these interactions entangles the macroscopic system with the environment, and the entanglement effectively destroys the coherence between branches of the superposition. What starts as

$$|\Psi\rangle = \frac{1}{\sqrt{2}}(|\text{decayed}\rangle|\text{dead}\rangle

• |\text{undecayed}\rangle|\text{alive}\rangle)$$

rapidly becomes, after environmental entanglement (tracing over environmental degrees of freedom $|E\rangle$):

$$\rho = \frac{1}{2}|\text{decayed}\rangle\langle\text{decayed}| \otimes |\text{dead}\rangle\langle\text{dead}|

• \frac{1}{2}|\text{undecayed}\rangle\langle\text{undecayed}| \otimes |\text{alive}\rangle\langle\text{alive}|.$$

This is a mixed state, not a superposition. The off-diagonal terms (the interference terms that distinguish a superposition from a classical mixture) vanish on a timescale

where $E_\mathrm{int}$ is the interaction energy with each environmental degree of freedom and $N$ is the number of such degrees of freedom. For a macroscopic object at room temperature, $\tau_\mathrm{decoherence}$ is of order $10^{-20}$–$10^{-30}$ seconds — unmeasurably short. The cat is never in a superposition for any observable duration. The superposition collapses before any measurement can resolve it.

This is not a philosophical solution to the measurement problem — it does not explain why a particular measurement outcome is obtained, only why we never observe interference between macroscopic branches — but it does explain why Schrödinger’s setup does not produce an observable macroscopic superposition. The cat’s entanglement with its own environment (the box, the air, its own thermal photons) destroys the coherence long before any observation.

What a Cat State Actually Is

In quantum optics, a cat state is not a cat in a superposition. It is a specific quantum state of a harmonic oscillator (typically a mode of the electromagnetic field) that was named in honour of Schrödinger’s thought experiment.

A coherent state $|\alpha\rangle$ is the quantum state that most closely resembles a classical oscillating electromagnetic field with amplitude $\alpha \in \mathbb{C}$. Coherent states are eigenstates of the annihilation operator: $\hat{a}|\alpha\rangle = \alpha|\alpha\rangle$. The mean photon number is $\bar{n} = |\alpha|^2$.

A cat state is a superposition of two coherent states with opposite phases:

where $\mathcal{N}_\pm = 1/\sqrt{2(1 \pm e^{-2|\alpha|^2})}$ is the normalisation constant. For large $|\alpha|$, the two coherent states are nearly orthogonal: $\langle -\alpha | \alpha \rangle = e^{-2|\alpha|^2} \approx 0$.

The Wigner quasi-probability distribution of a cat state is revealing. The Wigner function of a coherent state $|\alpha\rangle$ is a Gaussian peaked at $(x, p) = (\sqrt{2}\,\mathrm{Re}\,\alpha, \sqrt{2}\,\mathrm{Im}\,\alpha)$. The cat state Wigner function is:

$$W_{\mathrm{cat}+}(x,p) = \mathcal{N}+^2\bigl[W_{|\alpha\rangle}(x,p) + W_{|-\alpha\rangle}(x,p)

• 2W_\mathrm{int}(x,p)\bigr],$$

where the interference term $W_\mathrm{int}$ has negative values in the region between the two Gaussian peaks. Negative regions of the Wigner function are a signature of non-classical states; they cannot arise from any classical probability distribution. The cat state is quantum mechanical in a way that coherent states are not.

Haroche and the Nobel Prize

Serge Haroche (ENS Paris) spent two decades developing techniques to create, control, and observe cat states of the electromagnetic field in real time. His experiment used a superconducting microwave cavity — a polished copper box cooled to near absolute zero — in which single microwave photons could be trapped for hundreds of milliseconds, and a beam of single Rydberg atoms to probe the field non-destructively.

Haroche created cat states of cavity photons and, crucially, watched their decoherence in real time: as the quantum coherence between the two branches $|\alpha\rangle$ and $|-\alpha\rangle$ was progressively destroyed by coupling to the environment, the Wigner function’s negative region (the interference fringe) smoothed out and disappeared, leaving a classical mixture. The decoherence rate was proportional to $|\alpha|^2$ — the mean photon number, which measures how “macroscopic” the cat state is:

where $\kappa$ is the photon loss rate of the cavity. A larger cat (larger $|\alpha|^2$) decoheres faster, as Schrödinger’s argument implicitly requires.

Haroche shared the 2012 Nobel Prize in Physics with David Wineland “for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems.”

Cat Qubits: From Paradox to Engineering

The step from fundamental physics to quantum computing was taken when researchers noted that the two coherent states $|\alpha\rangle$ and $|-\alpha\rangle$ can serve as the two computational basis states of a qubit:

The cat qubit encodes a logical qubit in this pair of coherent states. Its remarkable property is an intrinsic asymmetry between error types.

Bit-Flip Suppression

A bit-flip error ($|0\rangle_L \leftrightarrow |1\rangle_L$, i.e., $|\alpha\rangle \leftrightarrow |-\alpha\rangle$) requires flipping the amplitude of the oscillator from $+\alpha$ to $-\alpha$. For a stabilised cat qubit (confined to the cat-state manifold by a parametric drive), this requires overcoming an energy barrier proportional to $|\alpha|^2$. The bit-flip time scales exponentially:

where $T_1$ is the single-photon loss time. For modest values of $|\alpha|^2$ (mean photon numbers of 5–10), the bit-flip time can exceed minutes.

A phase-flip error (the other error type) is not suppressed — the cat qubit is still vulnerable to dephasing at a rate proportional to $|\alpha|^2$. This creates a strongly biased noise channel: only one of the two error types is relevant.

The Engineering Consequence

Biased noise is useful because it allows the error-correcting code to focus its resources on only one error type. A repetition code (a string of cat qubits where phase errors are corrected by majority vote) can suppress the phase-flip error arbitrarily while the exponential bit-flip suppression handles the other. The hardware overhead for fault tolerance — the ratio of physical qubits to logical qubits — is dramatically reduced compared to codes that must handle both error types equally.

In 2023 and 2024, several groups demonstrated cat qubits with bit-flip times of seconds to minutes:

• Grimm et al. (2020, Nature 584, 205): Kerr cat qubit with exponential bit-flip suppression demonstrated in a superconducting circuit.
• Berdou et al. (2023, PRX Quantum 4, 020350): Cat qubit with $T_X$ exceeding $100$ seconds.
• Reglade et al. (2024, Nature 629, 778–783): Cat qubits from Alice & Bob demonstrating exponential scaling $T_\mathrm{bit-flip} \propto e^{2|\alpha|^2}$ with mean photon numbers up to $|\alpha|^2 \approx 10$, pushing bit-flip times beyond $10$ seconds in the laboratory and, in subsequent chip demonstrations, beyond several minutes.

This is the state of the art as of early 2025: the cat qubit is no longer a curiosity but a competitive architecture for fault-tolerant quantum computing, with bit-flip coherence times exceeding the best alternative approaches.

The Wigner Function and Quantum Non-Classicality

The Wigner quasi-probability distribution provides the most informative picture of a quantum state’s non-classicality. For a state with density matrix $\rho$, the Wigner function is:

For the cat state $|\mathrm{cat}_+\rangle$ with $|\alpha|^2 = 4$ (four mean photons in each coherent component), the Wigner function has two positive Gaussian peaks at $(x, p) = (\pm\sqrt{2}|\alpha|, 0)$ and an oscillating interference fringe between them with negative regions of amplitude $\sim -2/\pi$. The negativity of the Wigner function is a necessary condition for the state to exhibit quantum features that no classical mixture can reproduce.

As decoherence proceeds (e.g., through photon loss in a cavity), the negative regions shrink and eventually vanish — the Wigner function becomes everywhere non-negative, and the state becomes classically describable as a mixture of coherent states. This is the quantum-to-classical transition, made visible in phase space.

Haroche’s team measured this process directly, frame by frame, in real time. It is one of the most dramatic experimental visualisations of decoherence ever achieved.

What Schrödinger Would Make of This

Schrödinger was a physicist, not a philosopher of language. If told in 1935 that ninety years later, the superposition of two distinguishable states of a harmonic oscillator — named after his cat, with the same formal structure as his thought experiment — would be the leading candidate for the basic unit of a fault-tolerant quantum computer, he would have had two questions.

The first: how do you maintain the superposition against decoherence? The answer is that you work at millikelvin temperatures in superconducting circuits, and you use an active parametric drive to confine the state to the cat-state manifold.

The second, I think, would have been: does this resolve the measurement problem? And the honest answer remains: no, not fully. Decoherence explains why macroscopic superpositions are unobservable, but it does not explain why any particular measurement outcome occurs. That question is as open as it was in 1935.

What has changed is the practical relationship between quantum theory and technology. The uncertainty Schrödinger was pointing at — the strangeness of superposition, the fragility of coherence, the role of the environment — is now a resource to be engineered, not a conceptual embarrassment to be resolved. The cat qubit works precisely because the decoherence is asymmetric: bit flips are exponentially suppressed while phase flips are correctable. The asymmetry is exploited, not apologised for.

My two cats, meanwhile, are in definite classical states. One is on the radiator. The other is on the keyboard.

References

• Grimm, A., Frattini, N.E., Puri, S., Mundhada, S.O., Touzard, S., Mirrahimi, M., Girvin, S.M., Shankar, S., & Devoret, M.H. (2020). Stabilization and operation of a Kerr-cat qubit. Nature, 584, 205–209. https://doi.org/10.1038/s41586-020-2587-z

• Haroche, S., & Raimond, J.-M. (2006). Exploring the Quantum: Atoms, Cavities, and Photons. Oxford University Press.

• Reglade, U., Bocquet, A., Gautier, R., et al. (2024). Quantum control of a cat qubit with bit-flip times exceeding ten seconds. Nature, 629, 778–783. https://doi.org/10.1038/s41586-024-07294-3

• Mirrahimi, M., Leghtas, Z., Albert, V.V., Touzard, S., Schoelkopf, R.J., Jiang, L., & Devoret, M.H. (2014). Dynamically protected cat-qubits: A new paradigm for universal quantum computation. New Journal of Physics, 16, 045014. https://doi.org/10.1088/1367-2630/16/4/045014

• Schrödinger, E. (1935). Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften, 23(48), 807–812; 23(49), 823–828; 23(50), 844–849. https://doi.org/10.1007/BF01491891

• Walls, D.F., & Milburn, G.J. (2008). Quantum Optics (2nd ed.). Springer.

• Zurek, W.H. (2003). Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75(3), 715–775. https://doi.org/10.1103/RevModPhys.75.715

Changelog

• 2026-02-17: Updated “bit-flip times exceeding seven minutes” in the summary to “exceeding minutes,” aligning with the sourced figures: the body text reports “beyond several minutes” and Reglade et al. (2024) report “exceeding ten seconds.”