Unanswered Questions
245 questions with no upvoted or accepted answers
15
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679
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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 ...
- 1,502
12
votes
0
answers
347
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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 ...
- 14.4k
11
votes
0
answers
143
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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 ...
glS♦
- 26.9k
11
votes
0
answers
207
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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, ...
- 24.8k
10
votes
0
answers
110
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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 ...
glS♦
- 26.9k
10
votes
0
answers
219
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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
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286
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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, ...
- 3,493
8
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170
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How does the extremality of a POVM reflect on its Naimark dilation isometry?
Let $\mu:\Sigma\to\mathrm{Pos}(\mathbb{C}^d)$ be some POVM, with $\Sigma$ the finite set of possible outcomes, and $\mathrm{Pos}(\mathbb{C}^d)$ the set of $d$-dimensional positive semidefinite ...
glS♦
- 26.9k
8
votes
0
answers
284
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What are examples of zero capacity quantum channels with Choi rank less than $d$?
All the currently known examples of quantum channels with zero quantum capacity are either PPT or anti-degradable. These notions can be conveniently defined in terms of the Choi matrix of the given ...
- 24.8k
8
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0
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139
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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 $V$. ...
- 24.8k
8
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262
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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 ...
glS♦
- 26.9k
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 ...
- 397
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 ...
glS♦
- 26.9k
6
votes
0
answers
184
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Is it possible to obtain a closed-form expression of the diamond distance between two single-qubit channels?
I would like to compute the diamond norm of the difference of two single-qubit channels $\Phi_1$ and $\Phi_2$. This difference is equal to, for any $2\times2$ complex matrix $\rho$:
$$\...
- 3,493
6
votes
0
answers
247
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Why is combined amplitude and phase damping considered sufficient for noise modeling?
In QECC literature, I often come across the "combined amplitude and phase damping channel" as being representative of a realistic noise model which makes sense (as amplitude damping and de-...
glS♦
- 26.9k