Is there a Planck unit for minimum (but non-zero) amplitude for a quantum state, as well as a minimum (but non-zero)?

[quantumadmin]

In quantum mechanics, amplitudes are complex numbers that represent the probability coefficients of quantum states. The concept of quantization is deeply tied to the discretization of certain physical quantities in the quantum realm, such as energy levels in atomic systems. However, when it comes to amplitudes, the situation is a bit different.

Quantum mechanics doesn't inherently impose a discrete quantization of amplitudes like it does for some other properties. Instead, amplitudes can take on any complex value, including both real and imaginary parts. This continuous nature of amplitudes is a fundamental aspect of quantum mechanics.

Planck units, like the Planck length, time, and energy, represent fundamental scales at which quantum effects become important. However, there isn't a Planck unit for minimum non-zero amplitude or minimum difference between two amplitudes. The concept of amplitude is not subject to the same type of quantization as other properties.

It's important to understand that quantum mechanics operates in a probabilistic manner. The magnitudes of amplitudes are squared to calculate probabilities, and this squared magnitude represents the probability density associated with a particular quantum state. As a result, the physical significance of an individual amplitude value is less important than its relationship to other amplitudes within a quantum state.

While there isn't an absolute lower limit for the values of amplitudes, practical quantum computing systems do have limitations. Quantum hardware operates in a finite-dimensional Hilbert space, and due to factors like noise, decoherence, and finite precision, there are practical limits to the precision with which amplitudes can be manipulated and measured. However, these limitations are related to the technology and implementation of quantum hardware rather than a fundamental quantization of amplitudes themselves.

Certain properties in quantum mechanics are quantized, amplitudes of quantum states are not subject to the same type of quantization. They can take on continuous complex values, and any limitations on their precision are due to the constraints of the quantum hardware rather than a fundamental quantization.