65,276 research outputs found
Random private quantum states
The study of properties of randomly chosen quantum states has in recent years
led to many insights into quantum entanglement. In this work, we study private
quantum states from this point of view. Private quantum states are bipartite
quantum states characterised by the property that carrying out simple local
measurements yields a secret bit. This feature is shared by the maximally
entangled pair of quantum bits, yet private quantum states are more general and
can in their most extreme form be almost bound entangled. In this work, we
study the entanglement properties of random private quantum states and show
that they are hardly distinguishable from separable states and thus have low
repeatable key, despite containing one bit of key. The technical tools we
develop are centred around the concept of locally restricted measurements and
include a new operator ordering, bounds on norms under tensoring with entangled
states and a continuity bound for a relative entropy measure.Comment: v3: published version. v2: 13+7 pages, 1 figure, corrected
statements. v1: 16+8 pages, no figure
Authentication of Quantum Messages
Authentication is a well-studied area of classical cryptography: a sender S
and a receiver R sharing a classical private key want to exchange a classical
message with the guarantee that the message has not been modified by any third
party with control of the communication line. In this paper we define and
investigate the authentication of messages composed of quantum states. Assuming
S and R have access to an insecure quantum channel and share a private,
classical random key, we provide a non-interactive scheme that enables S both
to encrypt and to authenticate (with unconditional security) an m qubit message
by encoding it into m+s qubits, where the failure probability decreases
exponentially in the security parameter s. The classical private key is 2m+O(s)
bits. To achieve this, we give a highly efficient protocol for testing the
purity of shared EPR pairs. We also show that any scheme to authenticate
quantum messages must also encrypt them. (In contrast, one can authenticate a
classical message while leaving it publicly readable.) This has two important
consequences: On one hand, it allows us to give a lower bound of 2m key bits
for authenticating m qubits, which makes our protocol asymptotically optimal.
On the other hand, we use it to show that digitally signing quantum states is
impossible, even with only computational security.Comment: 22 pages, LaTeX, uses amssymb, latexsym, time
Experimental device-independent certified randomness generation with an instrumental causal structure
The intrinsic random nature of quantum physics offers novel tools for the
generation of random numbers, a central challenge for a plethora of fields.
Bell non-local correlations obtained by measurements on entangled states allow
for the generation of bit strings whose randomness is guaranteed in a
device-independent manner, i.e. without assumptions on the measurement and
state-generation devices. Here, we generate this strong form of certified
randomness on a new platform: the so-called instrumental scenario, which is
central to the field of causal inference. First, we theoretically show that
certified random bits, private against general quantum adversaries, can be
extracted exploiting device-independent quantum instrumental-inequality
violations. To that end, we adapt techniques previously developed for the Bell
scenario. Then, we experimentally implement the corresponding
randomness-generation protocol using entangled photons and active feed-forward
of information. Moreover, we show that, for low levels of noise, our protocol
offers an advantage over the simplest Bell-nonlocality protocol based on the
Clauser-Horn-Shimony-Holt inequality.Comment: Modified Supplementary Information: removed description of extractor
algorithm introduced by arXiv:1212.0520. Implemented security of the protocol
against general adversarial attack
Limitations for private randomness repeaters
Cryptographic protocols are often based on the two main resources: private
randomness and private key. In this paper, we develop a relationship between
these two resources. First, we show that any state containing perfect, directly
accessible, private key (a private state) is a particular case of the state
containing perfect, directly accessible, private randomness (an independent
state). We then demonstrate a fundamental limitation on the possibility of
transferring the privacy of random bits in quantum networks with an
intermediate repeater station. More precisely, we provide an upper bound on the
rate of repeated randomness in this scenario, similar to the one derived for
private key repeaters. This bound holds for states with positive partial
transposition. We further demonstrate the power of this upper bound by showing
a gap between the localisable and the repeated private randomness for separable
Werner states. In the case of restricted class of operations, we provide also a
bound on repeated randomness which holds for arbitrary states.Comment: 16 pages, 5 figures, close to published versio
On Simultaneous Information and Energy Transmission through Quantum Channels
The optimal rate at which information can be sent through a quantum channel
when the transmitted signal must simultaneously carry some minimum amount of
energy is characterized. To do so, we introduce the quantum-classical analogue
of the capacity-power function and generalize results in classical information
theory for transmitting classical information through noisy channels. We show
that the capacity-power function for a quantum channel, for both unassisted and
private protocol, is concave and also prove additivity for unentangled and
uncorrelated ensembles of input signals. This implies we do not need
regularized formulas for calculation. We numerically demonstrate these
properties for some standard channel models. We obtain analytical expressions
for the capacity-power function for the case of noiseless channels using
properties of random quantum states and concentration phenomenon in large
Hilbert spaces.Comment: 13 pages, 16 figure
Pseudorandomness with Proof of Destruction and Applications
Two fundamental properties of quantum states that quantum information theory explores are pseudorandomness and provability of destruction.
We introduce the notion of quantum pseudorandom states
with proofs of destruction (PRSPD) that combines both these properties.
Like standard pseudorandom states (PRS), these are efficiently
generated quantum states that are indistinguishable from random, but they can also be measured to create a classical string. This string is
verifiable (given the secret key) and certifies that the state has been destructed.
We show that, similarly to PRS, PRSPD can be constructed
from any post-quantum one-way function. As far as the authors are
aware, this is the first construction of a family of states that satisfies
both pseudorandomness and provability of destruction.
We show that many cryptographic applications that were shown
based on PRS variants using quantum communication can be based
on (variants of) PRSPD using only classical communication. This includes
symmetric encryption, message authentication, one-time signatures, commitments, and classically verifiable private quantum coins
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