20,847 research outputs found
(Pseudo) Random Quantum States with Binary Phase
We prove a quantum information-theoretic conjecture due to Ji, Liu and Song
(CRYPTO 2018) which suggested that a uniform superposition with random
\emph{binary} phase is statistically indistinguishable from a Haar random
state. That is, any polynomial number of copies of the aforementioned state is
within exponentially small trace distance from the same number of copies of a
Haar random state.
As a consequence, we get a provable elementary construction of
\emph{pseudorandom} quantum states from post-quantum pseudorandom functions.
Generating pseduorandom quantum states is desirable for physical applications
as well as for computational tasks such as quantum money. We observe that
replacing the pseudorandom function with a -wise independent function
(either in our construction or in previous work), results in an explicit
construction for \emph{quantum state -designs} for all . In fact, we show
that the circuit complexity (in terms of both circuit size and depth) of
constructing -designs is bounded by that of -wise independent
functions. Explicitly, while in prior literature -designs required linear
depth (for ), this observation shows that polylogarithmic depth suffices
for all .
We note that our constructions yield pseudorandom states and state designs
with only real-valued amplitudes, which was not previously known. Furthermore,
generating these states require quantum circuit of restricted form: applying
one layer of Hadamard gates, followed by a sequence of Toffoli gates. This
structure may be useful for efficiency and simplicity of implementation
Product structure of heat phase space and branching Brownian motion
A generical formalism for the discussion of Brownian processes with
non-constant particle number is developed, based on the observation that the
phase space of heat possesses a product structure that can be encoded in a
commutative unit ring. A single Brownian particle is discussed in a Hilbert
module theory, with the underlying ring structure seen to be intimately linked
to the non-differentiability of Brownian paths. Multi-particle systems with
interactions are explicitly constructed using a Fock space approach. The
resulting ring-valued quantum field theory is applied to binary branching
Brownian motion, whose Dyson-Schwinger equations can be exactly solved. The
presented formalism permits the application of the full machinery of quantum
field theory to Brownian processes.Comment: 32 pages, journal version. Annals of Physics, N.Y. (to appear
A quantum genetic algorithm with quantum crossover and mutation operations
In the context of evolutionary quantum computing in the literal meaning, a
quantum crossover operation has not been introduced so far. Here, we introduce
a novel quantum genetic algorithm which has a quantum crossover procedure
performing crossovers among all chromosomes in parallel for each generation. A
complexity analysis shows that a quadratic speedup is achieved over its
classical counterpart in the dominant factor of the run time to handle each
generation.Comment: 21 pages, 1 table, v2: typos corrected, minor modifications in
sections 3.5 and 4, v3: minor revision, title changed (original title:
Semiclassical genetic algorithm with quantum crossover and mutation
operations), v4: minor revision, v5: minor grammatical corrections, to appear
in QI
NMR Quantum Computation
In this article I will describe how NMR techniques may be used to build
simple quantum information processing devices, such as small quantum computers,
and show how these techniques are related to more conventional NMR experiments.Comment: Pedagogical mini review of NMR QC aimed at NMR folk. Commissioned by
Progress in NMR Spectroscopy (in press). 30 pages RevTex including 15 figures
(4 low quality postscript images
Quantum-noise--randomized data-encryption for WDM fiber-optic networks
We demonstrate high-rate randomized data-encryption through optical fibers
using the inherent quantum-measurement noise of coherent states of light.
Specifically, we demonstrate 650Mbps data encryption through a 10Gbps
data-bearing, in-line amplified 200km-long line. In our protocol, legitimate
users (who share a short secret-key) communicate using an M-ry signal set while
an attacker (who does not share the secret key) is forced to contend with the
fundamental and irreducible quantum-measurement noise of coherent states.
Implementations of our protocol using both polarization-encoded signal sets as
well as polarization-insensitive phase-keyed signal sets are experimentally and
theoretically evaluated. Different from the performance criteria for the
cryptographic objective of key generation (quantum key-generation), one
possible set of performance criteria for the cryptographic objective of data
encryption is established and carefully considered.Comment: Version 2: Some errors have been corrected and arguments refined. To
appear in Physical Review A. Version 3: Minor corrections to version
Rounding of a first-order quantum phase transition to a strong-coupling critical point
We investigate the effects of quenched disorder on first-order quantum phase
transitions on the example of the -color quantum Ashkin-Teller model. By
means of a strong-disorder renormalization group, we demonstrate that quenched
disorder rounds the first-order quantum phase transition to a continuous one
for both weak and strong coupling between the colors. In the strong coupling
case, we find a distinct type of infinite-randomness critical point
characterized by additional internal degrees of freedom. We investigate its
critical properties in detail, and we discuss broader implications for the fate
of first-order quantum phase transitions in disordered systems.Comment: 5 pages, 4 figure
Quantum divisibility test and its application in mesoscopic physics
We present a quantum algorithm to transform the cardinality of a set of
charged particles flowing along a quantum wire into a binary number. The setup
performing this task (for at most N particles) involves log_2 N quantum bits
serving as counters and a sequential read out. Applications include a
divisibility check to experimentally test the size of a finite train of
particles in a quantum wire with a one-shot measurement and a scheme allowing
to entangle multi-particle wave functions and generating Bell states,
Greenberger-Horne-Zeilinger states, or Dicke states in a Mach-Zehnder
interferometer.Comment: 9 pages, 5 figure
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