256 research outputs found
Loss-tolerant parity measurement for distant quantum bits
We propose a scheme to measure the parity of two distant qubits, while
ensuring that losses on the quantum channel between them does not destroy
coherences within the parity subspaces. This capability enables deterministic
preparation of highly entangled qubit states whose fidelity is not limited by
the transmission loss. The key observation is that for a probe electromagnetic
field in a particular quantum state, namely a superposition of two coherent
states of opposite phases, the transmission loss stochastically applies a
near-unitary back-action on the probe state. This leads to a parity measurement
protocol where the main effect of the transmission losses is a decrease in the
measurement strength. By repeating the non-destructive (weak) parity
measurement, one achieves a high-fidelity entanglement in spite of a
significant transmission loss
Efficient long distance quantum communication
Despite the tremendous progress of quantum cryptography, efficient quantum
communication over long distances (>1000km) remains an outstanding challenge
due to fiber attenuation and operation errors accumulated over the entire
communication distance. Quantum repeaters, as a promising approach, can
overcome both photon loss and operation errors, and hence significantly speedup
the communication rate. Depending on the methods used to correct loss and
operation errors, all the proposed QR schemes can be classified into three
categories (generations). Here we present the first systematic comparison of
three generations of quantum repeaters by evaluating the cost of both temporal
and physical resources, and identify the optimized quantum repeater
architecture for a given set of experimental parameters. Our work provides a
roadmap for the experimental realizations of highly efficient quantum networks
over transcontinental distances.Comment: Sreraman Muralidharan and Linshu Li contributed equally to this wor
Efficient quantum key distribution over a collective noise channel
We present two efficient quantum key distribution schemes over two different
collective-noise channels. The accepted hypothesis of collective noise is that
photons travel inside a time window small compared to the variation of noise.
Noiseless subspaces are made up of two Bell states and the spatial degree of
freedom is introduced to form two nonorthogonal bases. Although these protocols
resort to entangled states for encoding the key bit, the receiver is only
required to perform single-particle product measurements and there is no basis
mismatch. Moreover, the detection is passive as the receiver does not switch
his measurements between two conjugate measurement bases to get the key.Comment: 6 pages, 1 figure; the revised version of the paper published in
Phys. Rev. A 78, 022321 (2008). Some negligible errors on the error rates of
eavesdropping check are correcte
Deterministic and Efficient Three-Party Quantum Key Distribution
Quantum information processing is based on the laws of quantum physics and guarantees the unconditional security. In this thesis we propose an efficient and deterministic three-party quantum key distribution algorithm to establish a secret key between two users. Using the formal methodological approach, we study and model a quantum algorithm to distribute a secret key to a sender and a receiver when they only share entanglement with a trusted party but not with each other. It distributes a secret key by special pure quantum states using the remote state preparation and controlled gates. In addition, we employ the parity bit of the entangled pairs and ancillary states to help in preparing and measuring the secret states. Distributing a state to two users requires two maximally entangled pairs as the quantum channel and a two-particle von Neumann projective measurement. This protocol is exact and deterministic. It distributes a secret key of d qubits by 2d entangled pairs and on average d bits of classical communication. We show the security of this protocol against the entanglement attack and offer a method for privacy amplification. Moreover, we also study the problem of distributing Einstein-Podolsky-Rosen (EPR) in a metropolitan network. The EPR is the building block of entanglement-based and entanglement-assisted quantum communication protocols. Therefore, prior shared EPR pair and an authenticated classical channel allow two distant users to share a secret key. To build a network architecture where a centralized EPR source creates entangled states by the process of spontaneous parametric down-conversion (SPDC) then routes the states to users in different access networks. We propose and simulate a metropolitan optical network (MON) architecture for entanglement distribution in a typical telecommunication infrastructure. The architecture allows simultaneous transmission of classical and quantum signals in the network and offers a dynamic routing mechanism to serve the entire metropolitan optical network
Quantum Simulation Logic, Oracles, and the Quantum Advantage
Query complexity is a common tool for comparing quantum and classical
computation, and it has produced many examples of how quantum algorithms differ
from classical ones. Here we investigate in detail the role that oracles play
for the advantage of quantum algorithms. We do so by using a simulation
framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms
that solve some problems with the same success probability and number of
queries as the quantum algorithms. The framework can be simulated using only
classical resources at a constant overhead as compared to the quantum resources
used in quantum computation. Our results clarify the assumptions made and the
conditions needed when using quantum oracles. Using the same assumptions on
oracles within the simulation framework we show that for some specific
algorithms, like the Deutsch-Jozsa and Simon's algorithms, there simply is no
advantage in terms of query complexity. This does not detract from the fact
that quantum query complexity provides examples of how a quantum computer can
be expected to behave, which in turn has proved useful for finding new quantum
algorithms outside of the oracle paradigm, where the most prominent example is
Shor's algorithm for integer factorization.Comment: 48 pages, 46 figure
Deterministic construction of arbitrary states with quadratically increasing number of two-qubit gates
We propose a quantum circuit composed of gates and four single-qubit
gates to generate a state of three qubits. This circuit was then enhanced
by integrating two-qubit gates to create a state of four and five qubits.
After a couple of enhancements, we show that an arbitrary state can be
generated depending only on the degree of enhancement. The generalized formula
for the number of two-qubit gates required is given, showing that an -qubit
-state generation can be achieved with quadratically increasing number of
two-qubit gates. Also, the practical feasibility is discussed regarding photon
sources and various applications of gates
Quantum Proofs
Quantum information and computation provide a fascinating twist on the notion
of proofs in computational complexity theory. For instance, one may consider a
quantum computational analogue of the complexity class \class{NP}, known as
QMA, in which a quantum state plays the role of a proof (also called a
certificate or witness), and is checked by a polynomial-time quantum
computation. For some problems, the fact that a quantum proof state could be a
superposition over exponentially many classical states appears to offer
computational advantages over classical proof strings. In the interactive proof
system setting, one may consider a verifier and one or more provers that
exchange and process quantum information rather than classical information
during an interaction for a given input string, giving rise to quantum
complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum
analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit
some properties from their classical counterparts, they also possess distinct
and uniquely quantum features that lead to an interesting landscape of
complexity classes based on variants of this model.
In this survey we provide an overview of many of the known results concerning
quantum proofs, computational models based on this concept, and properties of
the complexity classes they define. In particular, we discuss non-interactive
proofs and the complexity class QMA, single-prover quantum interactive proof
systems and the complexity class QIP, statistical zero-knowledge quantum
interactive proof systems and the complexity class \class{QSZK}, and
multiprover interactive proof systems and the complexity classes QMIP, QMIP*,
and MIP*.Comment: Survey published by NOW publisher
New class of quantum error-correcting codes for a bosonic mode
We construct a new class of quantum error-correcting codes for a bosonic mode
which are advantageous for applications in quantum memories, communication, and
scalable computation. These 'binomial quantum codes' are formed from a finite
superposition of Fock states weighted with binomial coefficients. The binomial
codes can exactly correct errors that are polynomial up to a specific degree in
bosonic creation and annihilation operators, including amplitude damping and
displacement noise as well as boson addition and dephasing errors. For
realistic continuous-time dissipative evolution, the codes can perform
approximate quantum error correction to any given order in the timestep between
error detection measurements. We present an explicit approximate quantum error
recovery operation based on projective measurements and unitary operations. The
binomial codes are tailored for detecting boson loss and gain errors by means
of measurements of the generalized number parity. We discuss optimization of
the binomial codes and demonstrate that by relaxing the parity structure, codes
with even lower unrecoverable error rates can be achieved. The binomial codes
are related to existing two-mode bosonic codes but offer the advantage of
requiring only a single bosonic mode to correct amplitude damping as well as
the ability to correct other errors. Our codes are similar in spirit to 'cat
codes' based on superpositions of the coherent states, but offer several
advantages such as smaller mean number, exact rather than approximate
orthonormality of the code words, and an explicit unitary operation for
repumping energy into the bosonic mode. The binomial quantum codes are
realizable with current superconducting circuit technology and they should
prove useful in other quantum technologies, including bosonic quantum memories,
photonic quantum communication, and optical-to-microwave up- and
down-conversion.Comment: Published versio
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