16 votes
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What is the use of categorical quantum mechanics?

This answer is the opinion of someone who is essentially an outsider to "CQM" (= Categorical Quantum Mechanics), but a broadly sympathetic outsider. It should be interpreted as such. The motivations ...
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10 votes
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What exactly are Quantum XOR Games?

Quantum xor games are a method of greatly simplifying the ideas behind Bell's theorem, which states that no physical theory of local hidden variables can ever reproduce all of the predictions of ...
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8 votes
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What is the rank of a quantum channel?

Every quantum channel has many Kraus representations that may differ in the number of Kraus operators. For example, for any positive integer $n$ and numbers $p_i$ with $i=1,\dots,n$ and $\sum_{i=1}^...
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7 votes

Why do we need Hilbert spaces when talking about qubits and quantum computation?

Completeness ensures that Cauchy sequences have limits. This guarantees the existence of objects defined via limits of such sequences. These include derivatives, exponentials, trigonometric functions ...
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7 votes
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Are correlations stronger than those allowed by quantum mechanics possible?

Yes, it is possible to conceive theories with "stronger correlations" than those given by quantum mechanics. One way to make this statement precise is to consider some kind of "measurement apparatus" ...
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6 votes
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Why does quantum computing generally use matrix formulation of quantum mechanics rather than a continuous variable formulation?

Semantics aside, I’m assuming that your question is essentially “why do we use a matrix formulation of quantum mechanics rather than a continuous variable/differential equation/integral formulation” (...
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6 votes
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How can quantum interference happen in real world if a wave function does not have any physical meaning?

The assertion that the wavefunction has no physical meaning might mean different things in different contexts. Wavefunction is unobservable In one interpretation the assertion simply means that the ...
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5 votes
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How does the spectral decomposition of the Choi operator relate to Kraus operators?

Choi operator of a linear map $\mathcal{E}$ is defined as $$ J(\mathcal{E}) = \sum_{ij} \mathcal{E}(|i\rangle\langle j|)\otimes |i\rangle\langle j|.\tag1 $$ Substituting $\mathcal{E}(\rho)=\sum_k E_k\...
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5 votes

How to deal with entanglement relativistically?

The need for quantum fields There are two seemingly unrelated conceptual steps between quantum mechanics (QM) and quantum field theory (QFT). One step reconciles QM with special relativity (SR) and ...
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5 votes
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Difference between Bell's inequality and CHSH

The difference is as follows: the original Bell inequality requires that outcomes from the same setting are always perfectly anti-correlated. It says nothing about the case where they are even ...
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  • 47.5k
4 votes

Why does quantum computing generally use matrix formulation of quantum mechanics rather than a continuous variable formulation?

Quantum computing, in general, does not use Heisenberg's matrix mechanics or Dirac's interaction picture. I suggest that you carefully read the Wikipedia page on dynamical pictures. The differences ...
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4 votes
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What quantum gate is XNOR equivalent to?

There is no "standard" method to implement XNOR, but it can be logically obtained by attaching a NOT gate (often called an X gate in quantum computing) to a logical XOR (which you know is implemented ...
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  • 12.1k
4 votes
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What is the difference between no signaling and non locality at operational and ontological level?

I think the best way to understand this is by showing that one can violate (ontological) locality while respecting (operational) no-signalling. Take the case of Bohmian mechanics. In it the result of ...
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4 votes

What is the difference between no signaling and non locality at operational and ontological level?

No signaling means can't be used for communication. Can't be used to move messages from a sender to a receiver. Local means doesn't require communication to implement. Some processes, such as ...
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4 votes
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Effect of quantum entanglement on measurement

It depends on what exactly you mean by "affected". First of all, I'd say from your description that your "a" does not actually enter the discussion. The question is then ...
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4 votes
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Biggest variance of $h=\sum_i H_i$?

Here is an approach that requires no specific knowledge about $|\psi\rangle$ whatsoever. In your description you implied that each $H_i$ has the same maximum and minimum eigenvalues $\lambda_m$ and $\...
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  • 4,877
4 votes
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Can joint measurement be achieved in two labs far apart?

TL;DR No. Non-local gates and measurements between causally disconnected observers violate the no-signalling theorem and are therefore impossible. No-signalling theorem The following protocol allows ...
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3 votes

How does the spectral decomposition of the Choi operator relate to Kraus operators?

Let $M\in\mathrm{Lin}(\mathcal Y\otimes\mathcal X)$ be some linear operator whose input and output spaces are both $\mathcal Y\otimes\mathcal X$, for some pair of finite-dimensional Hilbert spaces $\...
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3 votes

Will two entangled qubits be affected by gravity?

Let's start with the Bell state $\frac1{\sqrt2}(|01\rangle+|10\rangle)$. Let's further assume that the entire universe (or at least the parts of relevance) are pervaded by a static magnetic field ...
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  • 608
3 votes

Superposition of quantum gates

Gate superposition Superposition is a complex linear combination of pure states with a physical interpretation of coefficients. One aspect of this interpretation concerns the probability of ...
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3 votes
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Why coherence measure monotonicity under selective incoherent operation should be form $C\left( \rho \right) \ge \sum_n{p_nC\left( \rho _n \right)}$?

These conditions aren't really related to coherence theory per se, they are directly inspired by the requirements that entanglement measures are typically required to satisfy, see e.g. the old review ...
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2 votes
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Equation for Quantum Gyroscopes

By a quantum gyroscope, it is usually meant a device or a sensor capable of measuring the same quantities as a classical gyroscope, namely angular velocities or orientations but with extremely higher ...
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2 votes
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Quantum teleportation and the reality of quantum states

The state of Bob's pair is not $1/2 (|0\rangle\langle0| + |1\rangle\langle1|)$. This is only his reduced density matrix. By definition, it is a representation of the locally accessible information Bob ...
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2 votes

Superposition of quantum gates

Just to sort of "talk out" the conceptual difficulty of a "superposition of gates" would be (which was discusssed in a more abstract way by @Adam Zalcman), let's try to ...
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2 votes

Superposition of quantum gates

This is nothing but a controlled-unitary gate. The only difference to an "ordinary" controlled-unitary is that now, the control qubit is encoded in the overall state of the device that ...
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2 votes

Can the Peres-Mermin square be reframed as a statement on the associated conditional outcome probabilities?

Duality of these two 'flavours' The non-existance of value assignments that are independent of the context of measurements is related to the non-existance of noncontextual ontological models for the ...
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  • 1,626
2 votes
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How to compute the eigenvector of this complex matrix in Grover's algorithm?

If I were you, I'd ignore the matrix $R$ and instead work with the matrix $Q$. They give you a conversion between vectors in the two different representations. First, I'm going to simplify things a ...
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2 votes
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For bipartite mixed state, if one part is pure, then the global mixed state is a product state?

Yes. Any mixed state $\rho$ is a convex combination of pure states, that is $$ \rho = \sum_i \lambda_i |\phi_i\rangle\langle\phi_i| $$ where $\lambda_i >0$, $\sum_i\lambda_i=1$. The partial trace ...
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  • 5,533
1 vote
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Why do we use 'modes' in quantum optics?

Modes are governed by eigenfunctions, I agree. In quantum optics, we need more than just eigenfunctions to describe a state of light: we need to know how many photons have properties corresponding to ...
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1 vote

How can quantum interference happen in real world if a wave function does not have any physical meaning?

I don't think it is particularly meaningful to say that a wavefunction "does not have physical meaning". It absolutely does: it tells you the probabilities of observing different outcomes in ...
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