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Here is another way to think about it. You can, in principle, store an infinite amount of information into a qubit, in the sense that you might need arbitrarily many bits to exactly pinpoint its stat …

The only difference between a "pair of qubits" and a single "four-dimensional qudit" is that when you say you have "two qubits" you are implicitly making some assumptions on the kind of operations you …

The only thing that is physical about a quantum state $|\psi\rangle$ is its square overlaps with other states. In other words, given an arbitrary complete basis $\{|u_k\rangle\}_k$, what matter are th …

The tensor product of a non-pure state with any other state gives a non-pure state. One way to see it is noticing that the von Neumann entropy is additive with respect to tensor products: $S(\rho\otim …

There is always an infinite number of measurement bases because there is an infinite number of orthonormal bases in any (more than one-dimensional) complex vector space. In fact, the set of all such b …

Let's say we take for granted that physical states are described by complex vectors $|\psi\rangle\in\mathbb C^n$ defined up to their normalisation and (global) phase. (Unitaries are the general way t …

Wave-particle duality is a general feature of quantum mechanics, see e.g. the relevant Wikipedia page, and this post on physics.SE. A "qubit" is an abstraction of a two-dimensional quantum system. W …

From a physical point of view, there couldn't be a bigger difference. Global phases are artefacts of the mathematical framework you are using, and have no physical meaning. Two states differing only …

Let $\rho\in\mathrm{D}(\mathcal H)$ be a state in some (finite-dimensional) Hilbert space $\mathcal H$ and suppose that $\operatorname{rank}(\rho)=r$. This means that we can write it as $$\rho = \sum_ …

I'll attempt here to provide a physical justification for why tensor products are the natural way to describe systems comprised of a number of different subsystems (e.g. a number of qubits). The takea …

One way to think about it is that "measuring in a given basis" is how we describe mathematically the act of interacting with the system in different ways. Taking as an example a qubit, "measuring in …

It strongly depends on your definition of have a value. What you might be referring to is the fact that qubits (and more in general quantum systems) can be in a state that, when measured in specific …

If by "corresponding state vector" you mean a pure state $\lvert\psi\rangle$ such that $\lvert\psi\rangle\!\langle\psi\rvert$ is maximally mixed, then the answer is that there isn't one. A density ma …

One way to understand the trace distance is to notice that it equals the (classical) trace distance (also referred to as Kolmogorov distance, see this post for some information about it) maximised ove …

(Case of pure states) Let $\rho=|\psi\rangle\!\langle\psi|$ be a pure bipartite state, suppose the underlying space is $\mathbb C^n\otimes\mathbb C^m$, and write as $|\psi\rangle=\sum_{k=1}^r \sqrt{p_ …