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Tagged with quantum-entanglement hilbert-space
163
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How do I prove that a reduced density matrix has properties of a density matrix?
The properties of a density matrix are defined as follows:
$(1) \ \ \mathrm{Tr}\rho = 1 $
$(2) \ \ \rho^\dagger = \rho $
$(3) \ \ \rho \ge 0 $
$(4) \ \ \mathrm{Tr}\rho^2 \le 1 $
A reduced density ...
CommunityBot
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When is a state entangled?
I have read from What's the difference between an entangled state, a superposed state and a cat state? that an entangled state is one that cannot be expressed as product state. Suppose we have the ...
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How can I construct a trivial product state in the continuum?
When working on the lattice it is easy to define a trivial product state. A state $|\psi\rangle$ is a trivial product state if it admits the following tensor decomposition,
\begin{equation}
|\psi\...
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Classical correlations in bipartite entangled mixed state
I have recently asked somewhat related question and got very illuminating answer. After some thinking however I have realized that (at least) one more point is unclear to me:
How can we check ...
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Seperable Quantum States
Some similar questions have been ask before, but I still don't really get the definition of seperable states in quantum mechanics.
Consider a bell state of a two qubit system.
\begin{align}
\left|\Psi\...
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Is maximal entanglement basis independent?
Is there a basis such that if we measure the bell state $\dfrac{|00\rangle+|11\rangle}{\sqrt2}$ the results might not be correlated at all (or at least not maximally)?
For example $\dfrac{|00\rangle+|...
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Can any bipartite state be written as $\rho_{AB}=\sum_{ij} p_{ij}\rho_A^i\otimes \rho_B^j$?
I'm having a silly doubt. If $\rho_{AB}$ is separable then we can write it as
$$ \rho_{AB}=\sum_i p_i\rho_A^i\otimes \rho_B^i$$
but can we write a general (maybe entangled) state as $$ \rho_{AB}=\sum_{...
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Why is the entanglement of formation upper bounded by the Schmidt number?
I have read many times in several articles (such as https://arxiv.org/abs/1609.05033) that the entanglement of formation EoF puts a lower bound on entanglement dimensionality $d$ (i.e., the Schmidt ...
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Computing Fubini-Study expectation values over $\mathbb{C}P^n$
In finite-dimensional textbook quantum mechanics, we postulate that states of our system are rays in a Hilbert space $\mathcal{H}$ with dimension $\dim{\mathcal{H}} = n+1$ where $n \in \mathbb{N}$, ...
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How does the many-worlds interpretation look like in bra ket notation?
If I understand correctly the many worlds interpretation says the universe is continously splitting into multiple branches and quantum measurements occur when decoherence causes a quantum state to ...
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What does doubly-entangled $W$-like state do with three-particle setup?
First, is entanglement of three particles in $W$-like state deliberately possible (and not by chance)? Second, is the following statement correct?
In the doubly entangled $W$ state, represented as
$$ |...
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How to determine parameters such that the state $|\psi\rangle=\frac1{\sqrt2}|+\rangle|+\rangle+a|+\rangle|x+\rangle+b|-\rangle|-\rangle$ is separable?
Suppose that two spin-1/2 are in the state:
$$ |\psi \rangle = \frac{1}{\sqrt{2}} |+\rangle|+\rangle + a|+\rangle|x+\rangle + b|-\rangle|-\rangle $$
and we want to find values for a & b such that ...
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How to measure the entanglement of three entangled qubits?
The entanglement of two qubits is calculated using "concurrence" and "negativity". Concurrence and negativity, however, are only used for "two" entangled qubits. Is there ...
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Path Integrals for entangled states
Is there a way of characterizing entanglement between states in a path integral formalism? If so, does this shed some light on the apparently non-local effects of quantum mechanics?
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How do I convert this separable state into a product state?
I know two particles in a Bell state cannot be written as a product state as they are entangled. But what if I had a classically correlated state$$\rho = \frac{1}{2}(|11\rangle\langle 11| + |00\rangle\...
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