For questions about the nonclassical properties of quantum systems, that is, properties of quantum systems that are incompatible with classical physics. Nonclassicality is a more general notion than that of entanglement, and the term can be used to loosely refer to different notions, such as nonlocality, steerability, non-Gaussianity, and many more.
Questions tagged [nonclassicality]
22 questions
14
votes
2 answers
Why doesn't the Gottesman-Knill theorem render quantum computing almost useless?
The Gottesman-Knill theore states (from Nielsen and Chuang)
Suppose a quantum computation is performed which involves only the following elements: state preparations in the computational basis, Hadamard gates, phase gates, controlled-NOT gates,…
user2723984
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13
votes
1 answer
How can classical bits be copied if qubits cannot be copied?
The no-cloning theorem of quantum mechanics tells us there can be no general quantum circuit that can copy arbitrary qubit states, i.e. a quantum gate or circuit cannot send $|0\rangle |\psi\rangle\mapsto|\psi\rangle |\psi\rangle$ for arbitrary…
MaximusIdeal
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11
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3 answers
Why are diagonal Hamiltonians considered classical?
I've been following UT QML course (http://localhost:8888/tree/UNI/PHD/UT-QML) and during their lecture on the Ising hamiltonian, they point out that the hamiltonian of an Ising model without a transverse field commutes
$$ H=-\sum_{} J_{ij}…
César Leonardo Clemente López
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7
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0 answers
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 ensemble $F^\star=\{\rho_\xi^\star\mathscr…
glS
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7
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1 answer
Circuit from finite group of gates and classical simulations
Let $ G $ be a finite group of quantum gates. Is it true that any circuit made using only gates from the finite group $ G $ can be efficiently simulated on a classical computer?
Here by circuit made from $ G $ I mean a circuit in which all gates…
Ian Gershon Teixeira
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7
votes
1 answer
Understanding Hardy's proof of "nonlocality without inequalities"
I'm reading the proof of "nonlocality without inequality" presented in (Hardy 1992).
In this protocol, we consider two particles (say, an electron and a positron) evolving almost independently: they both pass through one of two beamsplitters…
glS
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6
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1 answer
Are inseparable states with positive partial transpose nonlocal?
In Horodecki, Horodecki and Horodecki (1998), Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?, the authors remark in the conclusions (beginning of pag. 4, emphasis mine):
So, one is now faced with the problem…
glS
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6
votes
5 answers
Does a classical computer really require $2^n$ complex numbers to represent the state of $n$ qubit quantum computer?
One often reads that the key reason why classical computers (probabilistic or deterministic) are unable to simulate quantum algorithms such as Simon's or Shor's efficiently is that a classical computer needs $2^n$ complex numbers to represent an $n$…
QC-Novice
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5
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Defining joint-measurability on ensembles of states
Joint Measurability for a collection of POVMs $\{\Omega_j\}_j$ where $j$ is the index of the POVMs with associated effects $\{\Omega^\omega_j\}_{\omega}$ is defined as
$$\Omega^\omega_j = \sum_{\theta} p(\omega|j,\theta) \Theta^\theta,$$
where…
holl
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5
votes
2 answers
Why are commuting density operators said to be "classical states"?
In quantum information it is commonly said that a set of states $S=\{ \rho_i \}_i$ is classical if $[\rho_m, \rho_n] = 0, \,\forall \rho_m,\rho_n \in S$. This is meant in the sense that all observed behaviors (results from quantum measurements on…
cab20
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4
votes
2 answers
If classical physics emerges in some limit of quantum mechanics, shouldn't there be intermediate classical-quantum computers?
Presumably quantum mechanics really is the way the universe works, and it appears we don't really understand where the boundary between quantum mechanical phenomena like interference end and classical phenomena begin, but presumably it is not a…
Brandon
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4
votes
1 answer
What are some examples of uncomputability with quantum computers?
It is sometimes said that quantum effects lead to non computable results in the weak sense that quantum computers might allow truly random actions (at least according to some interpretations). I think this has been equated to quantum machines being…
Mauricio
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3
votes
1 answer
Classical and quantum limits to classical copying?
The no-cloning theorem can be sharpened to give quantitative bounds on the fidelity with which an arbitrary quantum state can be copied. Is there a similar picture available for classical copying? This breaks down into two
Questions:
In classical…
Tim Campion
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3
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2 answers
How is the additivity of accessible information, $\frac{1}{n} I_{\rm acc}(\rho^{\otimes n})=I_{\rm acc}(\rho)$, proved?
Let $\rho^{XA}$ be a classical-quantum state of the form
$$ \rho^{XA} = \sum_{x\in X} p_x |x\rangle\langle x|\otimes \rho_x^A, $$
and let the accessible information be given by
$$ I_{acc}(\rho^{XA}) = \sup_M I(X:Y), $$
where $M = \{M_y\}$ is a POVM…
user16106
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3
votes
3 answers
Does the CHSH inequality fully characterise the local polytope?
Consider the standard two-party CHSH scenario. Each party can perform one of two measurements (denoted with $x,y\in\{0,1\}$) and observe one of two outcomes (denoted with $a,b\in\{0,1\}$).
Let $P(ab|xy)$ be the probability of observing outcomes…
glS
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