Imaginary numbers first appeared in the 16^th century as a mathematical invention, introduced to solve equations that real numbers could not. As the name implies, many treated them as kind of trick to get results, rather than an underlying truth about the nature of reality. Although highly controversial at the time, these numbers are now ubiquitous in many fields of physics and mathematics.

One such field is quantum mechanics. Researchers routinely use complex numbers, which include both imaginary and real parts. For many simple quantum systems, you could think this is a mathematical convenience rather than a physical necessity. Predictions made with complex numbers can often be reproduced using only real numbers, albeit in a larger mathematical space.

The key question is: are complex numbers merely just a convenience, a trick, or are they necessary to understand complicated quantum systems? And if they are necessary, to what extent?

A team of researchers from France, Poland and Spain have been working on this problem and they’ve now come up with an answer. Their work relies on the composition postulate – a standard starting point for formulations of quantum mechanics which describes how quantum systems are combined mathematically.

They set out by studying a star-shaped quantum network. In this network, a number of outer parties (N) each receive one part of a quantum system, while a central party (Eve) receives the other parts from independent sources.

Each outer party chooses between several simple two-outcome measurements, while the central party performs one measurement with many possible outcomes.

Their strategy was to build a specially designed, conditional Bell test. The most well-known Bell test compares classical physics with quantum mechanics, with experiments demonstrating the latter is a better description of reality.  However, Bell tests can compare the correlations predicted by many other different theories.

The two theories studied here were standard quantum theory using complex numbers and a different formulation of the theory only using real numbers. While it was already shown that complex numbers are necessary, just how much the predictions of complex and real quantum theories differ is still an open question.

They found that the ratio between the predictions of the two theories increased proportional to N-1. So as the network gets larger, real-number quantum theory becomes increasingly bad at reproducing the results of standard complex-number quantum theory.

The work therefore gives a clear answer to the original question. Namely, in sufficiently large quantum networks, complex numbers provide an advantage that can become arbitrarily large. If the composition postulate is respected, they are physically required.

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Structured light is light with a designed spatial pattern. It can be shaped into standard topological structures, such as a twist in its phase or a changing polarisation across the beam. These patterns are useful because they can encode information, probe small distances and create topological field structures.

However, the issue is that is that these carefully engineered patterns often spread or degrade as the beam travels. This is a problem for real-world applications, such as precision metrology and super-resolution sensing.

In a new work, a team of researchers from Singapore and Spain went down a different route. They identified a spin structure which is both a topological texture and topological defect that is not laboriously engineered but appears automatically at the dark core of an optical vortex because Maxwell’s equations require it.

An optical vortex is a dark core in a light beam where the electric field vanishes. Because the field is zero there, the phase cannot be defined. The researchers found that the light around this core has a tiny, ordered spin pattern.

The called this a meronic spin defect. A meron is a texture that covers half of a sphere of possible spin directions, while a defect is a point where the direction becomes undefined. Here, both features occur together: the spin vanishes at the centre but forms a half-sphere-like pattern around it.

Crucially, these defects do not spread out during propagation. The beam might diffract as usual, but the normalised spin and polarisation patterns remain confined on subwavelength scales. They are also more stable against turbulence than standard engineered structures, because they arise intrinsically from Maxwell’s equations rather than from carefully balanced beam components.

Although still a fundamental result, the finding suggests that vortex cores could provide unusually stable and compact building blocks for future structured-light technologies.

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Most quantum computers today do not work in isolation. They rely on carefully timed signals from classical electronics, lasers or magnetic fields to tell the qubits when to perform each operation.

In ordinary quantum-computing theory, the qubits are treated as the computer while these timing signals are treated as external infrastructure. When calculating the energy required to run a quantum computer, drawing a boundary around the qubits like this will inevitably hide part of the real-world energy cost. Draw the boundary around the whole computing machine, including its clock, and a new energetic cost appears.

This is the idea behind new research from a team of researchers from Austria. In a new study, they introduced the idea of an autonomous quantum processing unit (aQPU). The aQPU has four main parts: a memory where the calculation happens, an instruction register that stores the program, a tick register that counts the steps, and an internal quantum clock that drives the whole process. The idea is similar to a mechanical machine that, once started, runs without an external operator.

The team showed there is an inescapable trade-off between accuracy and thermodynamics. If the clock ticks at slightly uncertain times, the quantum gates are applied imperfectly, reducing the fidelity of the computation. The authors found that the error grows with the length of the program and shrinks as the clock becomes more accurate. But more accurate clocks generally dissipate more entropy, meaning they produce more thermodynamic irreversibility.

In practice, such entropy production is usually associated with dissipated energy, often as heat. For quantum computers, this is especially awkward because many platforms already need delicate cooling and isolation procedures.

The new study does not propose a practical computer yet. Instead it gives physicists a cleaner way to ask how much energy quantum computation fundamentally requires. Even when quantum gates are mathematically reversible, the physical act of controlling them with sufficient precision may not be thermodynamically free.

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Exceptional points occur in open physical systems where two or more resonances merge so completely that both their measured values and their underlying states become identical. (Technically speaking, the eigenvalues and the eigenvectors coalesce.) Exceptional points are different from ordinary degeneracies, where two frequencies may be the same but the corresponding states remain separate.

Near an exceptional point, a tiny change in the system can produce a relatively large change in the resonances. That is why exceptional points have been proposed for sensitive devices such as optical sensors. But there is a catch: a large response is not automatically useful if quantum noise also increases at the same time.

In a new paper, researchers Jan Wiersig and Stefan Rotter tackled this problem using quantum Fisher information. This is a quantity that sets the best possible precision of a measurement under ideal conditions.

Their approach treats the sensor as a scattering device, where incoming coherent light is transformed into outgoing light, and asks how much information about a small perturbation can be extracted from that change.

The results are, unsurprisingly, complicated – but that complexity turns out to be revealing.

For several years, different groups have reached seemingly contradictory conclusions about whether exceptional points actually improve sensing at the quantum limit, with some studies reporting a clear advantage and others finding none. Wiersig and Rotter’s analysis helps explain these disagreements: the answer depends on the physical assumptions and, in particular, on how the input light, losses and perturbation are matched to the resonant modes.

The analysis therefore does not yield a simple yes-or-no verdict. Under suitably matched conditions, exceptional points can provide substantially more quantum Fisher information. For example, a factor-of-four enhancement for a second-order exceptional point in a two-microring system, and an even larger enhancement in the third-order case.

What’s more, the optimum operating point need not be the exceptional point itself. Moving slightly away from it can produce linewidth splitting, creating a longer-lived mode that interacts more strongly with the perturbation and thereby increases the useful signal.

The take-home message is that exceptional points are not magic sensitivity boosters. They can provide an advantage when the light field, perturbation and resonant mode are well matched. Internal losses may weaken or remove this advantage, although small losses do not destroy the overall picture.

Future exceptional-point sensors will therefore need to be designed as complete measurement systems, rather than around the exceptional point alone.

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