Tip of the Quantum Entropy Cone
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
Tip of the Quantum Entropy Cone. / Christandl, Matthias; Durhuus, Bergfinnur; Wolff, Lasse Harboe.
In: Physical Review Letters, Vol. 131, No. 24, 240201, 2023, p. 1-6.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Tip of the Quantum Entropy Cone
AU - Christandl, Matthias
AU - Durhuus, Bergfinnur
AU - Wolff, Lasse Harboe
PY - 2023
Y1 - 2023
N2 - Relations among von Neumann entropies of different parts of an N-partite quantum system have direct impact on our understanding of diverse situations ranging from spin systems to quantum coding theory and black holes. Best formulated in terms of the set Σ∗N of possible vectors comprising the entropies of the whole and its parts, the famous strong subaddivity inequality constrains its closure ¯Σ∗N, which is a convex cone. Further homogeneous constrained inequalities are also known. In this Letter we provide (nonhomogeneous) inequalities that constrain Σ∗N near the apex (the vector of zero entropies) of ¯Σ∗N, in particular showing that Σ∗N is not a cone for N≥3. Our inequalities apply to vectors with certain entropy constraints saturated and, in particular, they show that while it is always possible to upscale an entropy vector to arbitrary integer multiples it is not always possible to downscale it to arbitrarily small size, thus answering a question posed by Winter.
AB - Relations among von Neumann entropies of different parts of an N-partite quantum system have direct impact on our understanding of diverse situations ranging from spin systems to quantum coding theory and black holes. Best formulated in terms of the set Σ∗N of possible vectors comprising the entropies of the whole and its parts, the famous strong subaddivity inequality constrains its closure ¯Σ∗N, which is a convex cone. Further homogeneous constrained inequalities are also known. In this Letter we provide (nonhomogeneous) inequalities that constrain Σ∗N near the apex (the vector of zero entropies) of ¯Σ∗N, in particular showing that Σ∗N is not a cone for N≥3. Our inequalities apply to vectors with certain entropy constraints saturated and, in particular, they show that while it is always possible to upscale an entropy vector to arbitrary integer multiples it is not always possible to downscale it to arbitrarily small size, thus answering a question posed by Winter.
U2 - 10.1103/PhysRevLett.131.240201
DO - 10.1103/PhysRevLett.131.240201
M3 - Journal article
C2 - 38181127
VL - 131
SP - 1
EP - 6
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 24
M1 - 240201
ER -
ID: 375969621