34 research outputs found
An area law for the entropy of low-energy states
It is often observed in the ground state of spatially-extended quantum
systems with local interactions that the entropy of a large region is
proportional to its surface area. In some cases, this area law is corrected
with a logarithmic factor. This contrasts with the fact that in almost all
states of the Hilbert space, the entropy of a region is proportional to its
volume. This paper shows that low-energy states have (at most) an area law with
the logarithmic correction, provided two conditions hold: (i) the state has
sufficient decay of correlations, (ii) the number of eigenstates with vanishing
energy-density is not exponential in the volume. These two conditions are
satisfied by many relevant systems. The central idea of the argument is that
energy fluctuations inside a region can be observed by measuring the exterior
and a superficial shell of the region.Comment: 6 pages + appendix, 1 figur
Certified randomness in quantum physics
The concept of randomness plays an important role in many disciplines. On one
hand, the question of whether random processes exist is fundamental for our
understanding of nature. On the other hand, randomness is a resource for
cryptography, algorithms and simulations. Standard methods for generating
randomness rely on assumptions on the devices that are difficult to meet in
practice. However, quantum technologies allow for new methods for generating
certified randomness. These methods are known as device-independent because do
not rely on any modeling of the devices. Here we review the efforts and
challenges to design device-independent randomness generators.Comment: 18 pages, 3 figure
Key Distillation and the Secret-Bit Fraction
We consider distillation of secret bits from partially secret noisy
correlations P_ABE, shared between two honest parties and an eavesdropper. The
most studied distillation scenario consists of joint operations on a large
number of copies of the distribution (P_ABE)^N, assisted with public
communication. Here we consider distillation with only one copy of the
distribution, and instead of rates, the 'quality' of the distilled secret bits
is optimized, where the 'quality' is quantified by the secret-bit fraction of
the result. The secret-bit fraction of a binary distribution is the proportion
which constitutes a secret bit between Alice and Bob. With local operations and
public communication the maximal extractable secret-bit fraction from a
distribution P_ABE is found, and is denoted by Lambda[P_ABE]. This quantity is
shown to be nonincreasing under local operations and public communication, and
nondecreasing under eavesdropper's local operations: it is a secrecy monotone.
It is shown that if Lambda[P_ABE]>1/2 then P_ABE is distillable, thus providing
a sufficient condition for distillability. A simple expression for
Lambda[P_ABE] is found when the eavesdropper is decoupled, and when the honest
parties' information is binary and the local operations are reversible.
Intriguingly, for general distributions the (optimal) operation requires local
degradation of the data.Comment: 12 page
All bipartite entangled states display some hidden nonlocality
We show that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality
can be demonstrated in a certain kind of Bell experiment for all bipartite
entangled states. Our protocol allows local filtering measurements and involves
shared ancilla states that do not themselves violate CHSH. Our result follows
from two main steps. We first provide a simple characterization of the states
that violate the CHSH-inequality after local filtering operations in terms of
witness-like operators. Second, we prove that for each entangled state
, there exists another state not violating CHSH, such that
violates CHSH. Hence, in this scenario, cannot be
substituted by classical correlations without changing the statistics of the
experiment; we say that is not simulable by classical correlations and
our result is that entanglement is equivalent to non-simulability.Comment: 5 pages, 1 figur
Bell's inequalities detect efficient entanglement
We review the status of Bell's inequalities in quantum information, stressing
mainly the links with quantum key distribution and distillation of
entanglement. We also prove that for all the eavesdropping attacks using one
qubit, and for a family of attacks of two qubits, acting on half of a maximally
entangled state of two qubits, the violation of a Bell inequality implies the
possibility of an efficient secret-key extraction.Comment: 9 pages, for the Proceedings of EQIS'03 (Kyoto, Sept. 2003
A derivation (and quantification) of the third law of thermodynamics
The third law of thermodynamics has a controversial past and a number of
formulations due to Planck, Einstein, and Nernst. It's most accepted version,
the unattainability principle, states that "any thermodynamic process cannot
reach the temperature of absolute zero by a finite number of steps and within a
finite time." Although formulated in 1912, there has been no general proof of
the principle, and the only evidence we have for it is that particular cooling
methods become less efficient as the temperature decreases. Here we provide the
first derivation of a general unattainability principle, which applies to
arbitrary cooling processes, even those exploiting the laws of quantum
mechanics or involving an infinite-dimensional reservoir. We quantify the
resources needed to cool a system to any particular temperature, and translate
these resources into a minimal time or number of steps by considering the
notion of a Thermal Machine which obeys similar restrictions to universal
computers. We generally find that the obtainable temperature can scale as an
inverse power of the cooling time. Our argument relies on the heat capacity of
the bath being positive, and we show that if this is not the case then perfect
cooling in finite time is in principle possible. Our results also clarify the
connection between two versions of the third law (the Unattainability Principle
and the Heat Theorem), and place ultimate bounds on the speed at which
information can be erased.Comment: Substantial improvement of the third law derivation, which now only
relies on a single assumption: the positivity of the heat capacity. 7
pages+appendix, 2 figure