The entropy cones of $W_N$ and $W_N^d$ states
- URL: http://arxiv.org/abs/2204.04532v3
- Date: Sun, 19 Jun 2022 14:45:45 GMT
- Title: The entropy cones of $W_N$ and $W_N^d$ states
- Authors: Howard J. Schnitzer
- Abstract summary: The quantum entropy cones (QEC) for $W_N$ states of qubits and $W_Nd$ states of qudits are computed.
These cones emerge as symmetrized quantum entropy cones (SQEC) for arbitrary $N$ and $d$.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The quantum entropy cones (QEC) for $W_N$ states of qubits and $W_N^d$ states
of qudits are computed. These cones emerge as symmetrized quantum entropy cones
(SQEC) for arbitrary $N$ and $d$. Directed graph models are presented which
describe the SQEC for $W_N$ states and $W_N^d$ states. Monogamous mutual
information (MMI) is violated for all $N>3$.
Related papers
- Conditional entropy and information of quantum processes [0.7499722271664144]
We find that the conditional entropy of quantum channels has potential to reveal insights for quantum processes.
We identify a connection between the underlying causal structure of a bipartite channel and its conditional entropy.
arXiv Detail & Related papers (2024-10-02T16:50:47Z) - Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
We show how to reduce the geometry of degenerate states to the non-abelian connection $A$.
We find independent invariants associated with each triple of subspaces.
Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
arXiv Detail & Related papers (2024-04-04T06:39:28Z) - Comment on "Multiparty quantum mutual information: An alternative
definition" [0.0]
We show that, contrary to the claim by Kumar [Phys. Rev. A 96, 012332], the quantum dual total correlation of an $n$-partite quantum state cannot be represented.
We argue that the latter fails to yield a finite value for generalized $n$-partite Greenberger-Horne-Zeilinger states.
arXiv Detail & Related papers (2023-12-30T13:04:11Z) - $q$-analog qudit Dicke states [0.0]
We show that $q$-deformed qudit Dicke states can be compactly expressed as a weighted sum over permutations.
We also discuss the preparation of these states on a quantum computer, and show that introducing a $q$-dependence does not change the circuit gate count.
arXiv Detail & Related papers (2023-08-16T14:23:31Z) - Entanglement and Bell inequalities violation in $H\to ZZ$ with anomalous coupling [44.99833362998488]
We discuss entanglement and violation of Bell-type inequalities for a system of two $Z$ bosons produced in Higgs decays.
We find that a $ZZ$ state is entangled and violates the inequality for all values of the pair (anomalous) coupling constant.
arXiv Detail & Related papers (2023-07-25T13:44:31Z) - Tip of the Quantum Entropy Cone [1.1606619391009658]
Relations among von Neumann entropies of different parts of an $N$-partite quantum system have direct impact on our understanding of diverse situations.
We show that while it is always possible to up-scale an entropy vector to arbitrary integer multiples it is not always possible to down-scale it to arbitrarily small size.
arXiv Detail & Related papers (2023-05-31T21:37:24Z) - Quantum Speedups for Zero-Sum Games via Improved Dynamic Gibbs Sampling [30.53587208999909]
We give a quantum algorithm for computing an $epsilon$-approximate Nash equilibrium of a zero-sum game in a $m times n$ payoff matrix with bounded entries.
Given a standard quantum oracle for accessing the payoff matrix our algorithm runs in time $widetildeO(sqrtm + ncdot epsilon-2.5 + epsilon-3)$ and outputs a classical representation of the $epsilon$-approximate Nash equilibrium.
arXiv Detail & Related papers (2023-01-10T02:56:49Z) - Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann.
We show how our results have immediate applications to the modern theory of polarization.
arXiv Detail & Related papers (2022-05-30T18:01:34Z) - Quantum double aspects of surface code models [77.34726150561087]
We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry.
We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
arXiv Detail & Related papers (2021-06-25T17:03:38Z) - $k$-Uniform states and quantum information masking [15.308818907018546]
A pure state of $N$ parties with local dimension $d$ is called a $k$-uniform state if all the reductions to $k$ parties are maximally mixed.
We show that when $dgeq 4k-2$ is a prime power, there exists a $k$-uniform state for any $Ngeq 2k$ (resp. $2kleq Nleq d+1$)
arXiv Detail & Related papers (2020-09-26T01:27:45Z) - Bosonic quantum communication across arbitrarily high loss channels [68.58838842613457]
A general attenuator $Phi_lambda, sigma$ is a bosonic quantum channel that acts by combining the input with a fixed environment state.
We show that for any arbitrary value of $lambda>0$ there exists a suitable single-mode state $sigma(lambda)$.
Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity.
arXiv Detail & Related papers (2020-03-19T16:50:11Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.