1,943 research outputs found
A Tight High-Order Entropic Quantum Uncertainty Relation With Applications
We derive a new entropic quantum uncertainty relation involving min-entropy.
The relation is tight and can be applied in various quantum-cryptographic
settings.
Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit
Commitment are presented and the uncertainty relation is used to prove the
security of these protocols in the bounded quantum-storage model according to
new strong security definitions.
As another application, we consider the realistic setting of Quantum Key
Distribution (QKD) against quantum-memory-bounded eavesdroppers. The
uncertainty relation allows to prove the security of QKD protocols in this
setting while tolerating considerably higher error rates compared to the
standard model with unbounded adversaries. For instance, for the six-state
protocol with one-way communication, a bit-flip error rate of up to 17% can be
tolerated (compared to 13% in the standard model).
Our uncertainty relation also yields a lower bound on the min-entropy key
uncertainty against known-plaintext attacks when quantum ciphers are composed.
Previously, the key uncertainty of these ciphers was only known with respect to
Shannon entropy.Comment: 21 pages; editorial changes, additional applicatio
Entropic uncertainty relations - A survey
Uncertainty relations play a central role in quantum mechanics. Entropic
uncertainty relations in particular have gained significant importance within
quantum information, providing the foundation for the security of many quantum
cryptographic protocols. Yet, rather little is known about entropic uncertainty
relations with more than two measurement settings. In this note we review known
results and open questions.Comment: 12 pages, revte
Entropic uncertainty relations for quantum information scrambling
How violently do two quantum operators disagree? Different fields of physics
feature different measures of incompatibility: (i) In quantum information
theory, entropic uncertainty relations constrain measurement outcomes. (ii) In
condensed matter and high-energy physics, the out-of-time-ordered correlator
(OTOC) signals scrambling, the spread of information through many-body
entanglement. We unite these measures, proving entropic uncertainty relations
for scrambling. The entropies are of distributions over weak and strong
measurements' possible outcomes. The weak measurements ensure that the OTOC
quasiprobability (a nonclassical generalization of a probability, which
coarse-grains to the OTOC) governs terms in the uncertainty bound. The
quasiprobability causes scrambling to strengthen the bound in numerical
simulations of a spin chain. This strengthening shows that entropic uncertainty
relations can reflect the type of operator disagreement behind scrambling.
Generalizing beyond scrambling, we prove entropic uncertainty relations
satisfied by commonly performed weak-measurement experiments. We unveil a
physical significance of weak values (conditioned expectation values): as
governing terms in entropic uncertainty bounds.Comment: Close to published version, but has more-pedagogical formatting. 13
pages, including 4 figure
Experimental test of an entropic measurement uncertainty relation for arbitrary qubit observables
A tight information-theoretic measurement uncertainty relation is
experimentally tested with neutron spin-1/2 qubits. The noise associated to the
measurement of an observable is defined via conditional Shannon entropies and a
tradeoff relation between the noises for two arbitrary spin observables is
demonstrated. The optimal bound of this tradeoff is experimentally obtained for
various non-commuting spin observables. For some of these observables this
lower bound can be reached with projective measurements, but we observe that,
in other cases, the tradeoff is only saturated by general quantum measurements
(i.e., positive-operator valued measures), as predicted theoretically.Comment: 6 pages, 3 figure
A transform of complementary aspects with applications to entropic uncertainty relations
Even though mutually unbiased bases and entropic uncertainty relations play
an important role in quantum cryptographic protocols they remain ill
understood. Here, we construct special sets of up to 2n+1 mutually unbiased
bases (MUBs) in dimension d=2^n which have particularly beautiful symmetry
properties derived from the Clifford algebra. More precisely, we show that
there exists a unitary transformation that cyclically permutes such bases. This
unitary can be understood as a generalization of the Fourier transform, which
exchanges two MUBs, to multiple complementary aspects. We proceed to prove a
lower bound for min-entropic entropic uncertainty relations for any set of
MUBs, and show that symmetry plays a central role in obtaining tight bounds.
For example, we obtain for the first time a tight bound for four MUBs in
dimension d=4, which is attained by an eigenstate of our complementarity
transform. Finally, we discuss the relation to other symmetries obtained by
transformations in discrete phase space, and note that the extrema of discrete
Wigner functions are directly related to min-entropic uncertainty relations for
MUBs.Comment: 16 pages, 2 figures, v2: published version, clarified ref [30
Majorization uncertainty relations for mixed quantum states
Majorization uncertainty relations are generalized for an arbitrary mixed
quantum state of a finite size . In particular, a lower bound for the
sum of two entropies characterizing probability distributions corresponding to
measurements with respect to arbitrary two orthogonal bases is derived in terms
of the spectrum of and the entries of a unitary matrix relating both
bases. The obtained results can also be formulated for two measurements
performed on a single subsystem of a bipartite system described by a pure
state, and consequently expressed as uncertainty relation for the sum of
conditional entropies.Comment: 13 pages, 7 figure
Entropic Energy-Time Uncertainty Relation
Energy-time uncertainty plays an important role in quantum foundations and
technologies, and it was even discussed by the founders of quantum mechanics.
However, standard approaches (e.g., Robertson's uncertainty relation) do not
apply to energy-time uncertainty because, in general, there is no Hermitian
operator associated with time. Following previous approaches, we quantify time
uncertainty by how well one can read off the time from a quantum clock. We then
use entropy to quantify the information-theoretic distinguishability of the
various time states of the clock. Our main result is an entropic energy-time
uncertainty relation for general time-independent Hamiltonians, stated for both
the discrete-time and continuous-time cases. Our uncertainty relation is
strong, in the sense that it allows for a quantum memory to help reduce the
uncertainty, and this formulation leads us to reinterpret it as a bound on the
relative entropy of asymmetry. Due to the operational relevance of entropy, we
anticipate that our uncertainty relation will have information-processing
applications.Comment: 6 + 9 pages, 2 figure
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