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Sep
30
awarded  Explainer
Sep
27
answered If two quantum two-party states have the same entanglement, can they be transformed into each other by local unitary operation?
Aug
11
awarded  Yearling
Jan
19
answered Low rank entangled states
Jan
18
comment What is “k-Local Hamiltonian Problem” in quantum complexity theory?
See en.wikipedia.org/wiki/QMA#The_local_Hamiltonian_problem
Jan
10
revised Mapping a given density matrix to the generalized 2-qubit state
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Jan
10
answered Mapping a given density matrix to the generalized 2-qubit state
Dec
11
comment Solving Systems of Partial Trace Equations
@Adrian Good. So the hardness result I was referring to is arxiv.org/abs/quant-ph/0604166: Checking consistency of density matrix (i.e. whether there exists a global state consistent with the RDMs) is QMA-hard, i.e., hard to solve even for a quantum computer. --- A related remark: The corresponding problem for fermions is known as the N-representability problem, and has received a lot of attention in quantum chemistry.
Dec
10
comment Solving Systems of Partial Trace Equations
@Adrian The general problem (determining whether there is a state compatible with certain reduced states) is known as the "quantum marginal problem", and there has been quite some work on that. However, there the RDMs usually overlap etc., I'm not sure if that's what you're after.
Dec
10
comment Solving Systems of Partial Trace Equations
@Adrian Well, apparently you're not entirely happy with the answer of Trimok, so you must have sth. more specific in mind. Are you e.g. interested in a pure state? Then, the eigenvalues of the two RDMs must be equal. The general multipartite case is computationally hard. But the way it is phrased now, it seems very difficult to give a clear answer.
Dec
9
comment Solving Systems of Partial Trace Equations
@Adrian I think you should be a bit more precise with your question, then.
Nov
25
comment Discord for partially decohered bell state
The Mathematica code cannot be viewed without requesting some kind of permission.
Nov
24
comment Discord for partially decohered bell state
Your state $\psi_{AB}$ is not the same as Zurek's partially decohered Bell state in Eq. (17). (In particular, the latter is a mixed state.)
Nov
2
comment How does Landauer's Principle apply in quantum (and generally reversible) computing
... you might also want to check arxiv.org/abs/1306.4352.
Nov
2
comment How does Landauer's Principle apply in quantum (and generally reversible) computing
Yes, no, and no. Initializing one qubit dissipates $kT$ of energy, and thus, initializing N qubits dissipates an energy of $NkT$. (Note that if the energy would not scale linearly with the number of qubits, this would likely give rise to all kind of contradictions!) This is closely related to the question whether $N$ qubits "contain" $N$ bits or $2^N$ bits of information (and typically $N$ is the more appropriate answer) -- e.g., arxiv.org/abs/quant-ph/0507242 contains some arguments about that.
Aug
22
comment Definition of 'Majorana Number' in the Kitaev Chain
Definition of the Pfaffian (including the sign): en.wikipedia.org/wiki/Pfaffian (First equation in the Section "Formal definition".) You get Pfaffians when you normal order fermionic operators.
Aug
11
awarded  Yearling
May
22
comment Precise statement of Mermin–Wagner theorem
Is scholarpedia.org/article/Mermin-Wagner_Theorem of any help?
May
21
comment Why is this not a realisable operation on a quantum system?
You should read up on some basics of quantum information ... it is $\left[\begin{matrix}1&0&0&1\\0&0&0&0\\0&0&0&0\\1&0&0&1\end{matrix}\right]/2$, and you want to apply $\phi\otimes I$, i.e., you apply $\phi$ to every $2\times 2$ block individually. For $\phi$ to be a physical operation, the resulting state must be positive.
May
21
revised Why is this not a realisable operation on a quantum system?
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