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Unanswered Questions

162 questions with no upvoted or accepted answers
15 votes
0 answers
679 views

Relation between quantum entanglement and quantum state complexity

Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds ...
12 votes
0 answers
347 views

What is the Generalized Quantum Stein's Lemma and why is it important?

I'm sensing a lot of buzz about potential re-proofs of the Generalized Quantum Stein's Lemma - a generalization of the quantum counterpart to the classical Stein's Lemma, which is of some importance ...
11 votes
0 answers
143 views

Are there separable $\rho$ that cannot be decomposed with less than $\operatorname{rank}(\rho)^2$ pure product states?

In What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?, examples were given of separable states $\rho$ with separable decompositions requiring ...
11 votes
0 answers
207 views

Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities

For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, ...
10 votes
0 answers
110 views

Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ...
10 votes
0 answers
219 views

Entanglement transfer of spin-entangled triplet-pair states between flying qubits and stationary qubits

The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin ...
8 votes
0 answers
286 views

Five qubits can be entangled in how many ways?

It is well-known that there are two ways to entangle three qubits and nine ways to entangle four qubits. In page 22 of this paper I found that there are infinitely many ways to entangle five qubits, ...
8 votes
0 answers
139 views

Query on Reduced Graph States

Reduced graph states are characterized as follows (from page 46 of this paper): Let $A \subseteq V$ be a subset of vertices of a graph $G = (V,E)$ and $B = V\setminus A$ the complement of $A$ in $V$. ...
8 votes
0 answers
262 views

How can blackholes be fast information scramblers?

I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given. As mentioned by L. Susskind et. al, the fast scrambling ...
7 votes
0 answers
337 views

What is the motivation for Weyl matrices in quantum information theory?

Quantum Entanglement and Geometry — Andreas Gabriel (2010) — Sec: 2.3.4 ~p. 11 Another basis for $d\times d$-dimensional matrices that has proven to be quite useful in quantum information theory is ...
7 votes
0 answers
62 views

Construction of optimal ensemble to show quantum steerability

In Wiseman et al. (2007), in the process of deriving necessary and sufficient conditions for the steerability of some classes of states, the authors show (lemma 1, page 3) how to construct an optimal ...
6 votes
0 answers
432 views

Verification of local unitary equivalence between two pure states

This might be a non-trivial and hard problem. I've been thinking about this for days but couldn't find a good answer, so I hope any of you could give me a good answer/intuition for me to move forward. ...
6 votes
0 answers
105 views

Photon Entanglement using SPDC

Are there any good references where from I can learn about photon entanglement using spontaneous parametric down-conversion (SPDC)?
5 votes
0 answers
261 views

Explanation of the generalized SWAP test: the permutation test?

I am reading this paper on the state separability problem, and came across the term “Permutation Test.” This is on page 7 section 2.3. Apparently, the more famous SWAP test is a special case of ...
5 votes
0 answers
209 views

How to get to the formula for the entanglement of formation of two-qubit states?

An explicit formula for the entanglement of formation $E(\rho)$ for an arbitrary two-qubit state $\rho$ was given by Wooters in Entanglement of Formation of an Arbitrary State of Two Qubits. The ...

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