Research Articles:

**A new relativistic orthogonal states quantum key
distribution protocol**
(pp1081-1088)

Jordan S. Cotler
and Peter W. Shor

We introduce a new relativistic orthogonal states quantum key
distribution protocol which leverages the properties of both quantum
mechanics and special relativity to securely encode multiple bits onto
the spatio-temporal modes of a single photon. If the protocol is
implemented using a single photon source, it can have a key generation
rate faster than the repetition rate of the source, enabling faster
secure communication than is possible with existing protocols. Further,
we provide a proof that the protocol is secure and give a method of
implementing the protocol using line-of-sight and fiber optic channels.

**A quantum lower bound for distinguishing random
functions from random permutations**
(pp1089-1097)

Henry Yuen

The problem of distinguishing between a random function and a random
permutation on a domain of size $N$ is important in theoretical
cryptography, where the security of many primitives depend on the
problem's hardness. We study the quantum query complexity of this
problem, and show that any quantum algorithm that solves this problem
with bounded error must make $\Omega(N^{1/5}/\polylog N)$ queries to the
input function. Our lower bound proof uses a combination of the
Collision Problem lower bound and Ambainis's adversary theorem.

**Small sets of locally indistinguishable orthogonal
maximally entangled states**
(pp1098-1106)

Alessandro
Cosentino and Vincent Russo

We study the problem of distinguishing quantum states using local
operations and classical communication (LOCC). A question of fundamental
interest is whether there exist sets of $k \leq d$ orthogonal maximally
entangled states in $\complex^{d}\otimes\complex^{d}$ that are not
perfectly distinguishable by LOCC. A recent result by Yu, Duan, and Ying
[Phys. Rev. Lett. 109 020506 (2012)] gives an affirmative answer for the
case $k = d$. We give, for the first time, a proof that such sets of
states indeed exist even in the case $k < d$. Our result is constructive
and holds for an even wider class of operations known as
positive-partial-transpose measurements (PPT). The proof uses the
characterization of the PPT-distinguishability problem as a semidefinite
program.

**Entanglement-assisted quantum codes achieving the
quantum singleton bound but violating the quantum hamming bound**
(pp1107-1116)

Ruihu Li,
Luobin Guo, and Zongben Xu

We give an infinite family of degenerate entanglement-assisted
quantum error-correcting codes (EAQECCs) which violate the EA-quantum
Hamming bound for non-degenerate EAQECCs and achieve the EA-quantum
Singleton bound, thereby proving that the EA-quantum Hamming bound does
not asymptotically hold for degenerate EAQECCs. Unlike the previously
known quantum error-correcting codes that violate the quantum Hamming
bound by exploiting maximally entangled pairs of qubits, our codes do
not require local unitary operations on the entangled auxiliary qubits
during encoding. The degenerate EAQECCs we present are constructed from
classical error-correcting codes with poor minimum distances, which
implies that, unlike the majority of known EAQECCs with large minimum
distances, our EAQECCs take more advantage of degeneracy and rely less
on the error correction capabilities of classical codes.

**Study on error reconciliation in quantum key
distribution**
(pp1117-1135)

Qiong Li,
Dan Le, Haokun Mao, Xiamu Niu, Tian Liu, and Hong Guo

As one of the most important procedure in quantum key distribution
system, the error reconciliation algorithm has drew many attentions.
However, studies on the error reconciliation algorithm mainly focuses on
the reconciliation efficiency. Since the ultimate goal of study on the
error reconciliation is to find the most suitable algorithm for a
quantum key distribution system and maximize the throughput rate of the
whole system, the indicator of reconciliation efficiency is not
full-scale enough to evaluate an error reconciliation algorithm. In this
paper we propose a new evaluation scheme, including four direct
indicators and one composite indicator to solve the problem. Following
the new scheme, seven representative error reconciliation algorithms are
simulated and compared thoroughly, i.e. BBBSS, the original Cascade and
two improved Cascade algorithms, Winnow, and two LDPC based algorithms.
Our works are very beneficial to the evaluation, comparison, selection
and optimization of error reconciliation algorithms for a practical
quantum key distribution system.

**Quasiparticle localisation via frequent
measurements**
(pp1136-1148)

David A.
Herrera-Marti, Ying Li, and Leong Chuan Kwek

Topological quantum memories in two dimensions are not thermally
stable, since once a quasiparticle excitation is created, it will
delocalise at no energy cost. This places an upper bound on the lifetime
of quantum information stored in them. We address this issue for a
topological subsystem code introduced in [Bravyi S.{\em et al.},
Quant.~Inf.~Comp.~13(11):0963]. By frequently measuring the gauge
operators of the code, a technique known as Operator Quantum Zeno Effect
[Li Y. {\em et al.}, preprint arXiv:1305.2464], the dynamics responsible
for quasiparticle motion is suppressed, and can eventually be ``frozen"
in the large frequency limit. A feature of this method is that the
density operator of the code does not commute with the measurement
operators, so the density matrix will be randomised after a few
measurements. However the logical operators commute with the measurement
operators and are thus protected.

**Hardness of classically simulating quantum
circuits with unbounded Toffoli and fan-out gates**
(pp1149-1164)

Yasuhiro
Takahashi, Takeshi Yamazaki, and Kazuyuki Tanaka

We study the classical simulatability of constant-depth
polynomial-size quantum circuits followed by only one single-qubit
measurement, where the circuits consist of universal gates on at most
two qubits and additional gates on an unbounded number of qubits. First,
we consider unbounded Toffoli gates as additional gates and deal with
the weak simulation, i.e., sampling the output probability distribution.
We show that there exists a constant-depth quantum circuit with only one
unbounded Toffoli gate that is not weakly simulatable, unless $\bqp
\subseteq \postbpp \cap \am$. Then, we consider unbounded fan-out gates
as additional gates and deal with the strong simulation, i.e., computing
the output probability. We show that there exists a constant-depth
quantum circuit with only two unbounded fan-out gates that is not
strongly simulatable, unless $\p = \pp$. These results are in contrast
to the fact that any constant-depth quantum circuit without additional
gates on an unbounded number of qubits is strongly and weakly
simulatable.

**One-dimensional quantum walks via generating
function and the CGMV method**
(pp1165-1186)

Norio Konno
and Etsuo Segawa

We treat quantum walk (QW) on the line whose quantum coin at each
vertex tends to the identity as the distance goes to infinity. We
obtain a limit theorem that this QW exhibits localization with not an
exponential but a ``power-law" decay around the origin and a ``strongly"
ballistic spreading called bottom localization in this paper. This limit
theorem implies the weak convergence with linear scaling whose density
has two delta measures at $x=0$ (the origin) and $x=1$ (the bottom)
without continuous parts.

**Decoding in hyperbolic spaces: quantum LDPC codes
with linear rate and efficient error correction**
(pp1187-1202)

Matthew B.
Hastings

We analyze the four dimensional toric code in a hyperbolic space and
show that it has a classical error correction procedure which runs in
almost linear time and can be parallelized to almost constant time,
giving an example of a quantum LDPC code with linear rate and efficient
error correction.

**Multiplicativity of superoperator norms for some
entanglement breaking channels**
(pp1203-1212)

Christopher
King

It is known that the minimal output entropy is additive for any
product of entanglement breaking (EB) channels. The same is true for the
Renyi entropy, where additivity is equivalent to multiplicativity of the
\norm{1}{q} norm for all $q \ge 1$. In this paper we consider the
related question of multiplicativity of the \norm{2}{q} norm for $q > 2$
for entanglement breaking channels. We prove that multiplicativity holds
in this case for certain classes of EB channels, including both the CQ
and QC channels.

**Stability of point spectrum for three-state
quantum walks on a line**
(pp1213-1226)

Martin
Štefaňák, Iva Bezděková, Igor Jex, and Stephen M. Barnett

Evolution operators of certain quantum walks possess, apart from the
continuous part, also a point spectrum. The existence of eigenvalues and
the corresponding stationary states lead to partial trapping of the
walker in the vicinity of the origin. We analyze the stability of this
feature for three-state quantum walks on a line subject to homogenous
coin deformations. We find two classes of coin operators that preserve
the point spectrum. These new classes of coins are generalizations of
coins found previously by different methods and shed light on the rich
spectrum of coins that can drive discrete-time quantum walks.

**Relevance of rank for a mixed state quantum
teleportation resource**
(pp1227-1237)

K.G.
Paulson and S.V.M. Satyanarayana

Mixed entangled states are generic resource for quantum
teleportation. Optimal teleportation fidelity measures the success of
quantum teleportation. The relevance of rank in the teleportation
process is investigated by constructing three new maximally entangled
mixed states (MEMS) of different ranks. Linear entropy, concurrence,
optimal teleportation fidelity and Bell function are obtained for each
of these states analytically. It is found that mixed states with higher
rank are better resource for teleportation. In order to achieve a fixed
value of optimal teleportation fidelity, we find that low rank states
must have high concurrence. Further, for each of ranks 2, 3 and 4, we
numerically generate 30000 maximally entangled mixed states. The
analysis of these states reveals the existence of a rank dependent upper
bound on optimal teleportation fidelity for a fixed purity. In order to
achieve a fixed optimal teleportation fidelity, we find MEMS exhibit a
rank dependent lower bound on concurrence. MEMS are classified in terms
of their degree of nonlocality. The results are found to be same with
logarithmic negativity used as a measure of entanglement.

**Quantum network exploration with a faulty sense of
direction**
(pp1238-1250)

Jaroslaw A.
Miszczak and Przemyslaw Sadowski

We develop a model which can be used to analyse the scenario of
exploring quantum network with a distracted sense of direction. Using
this model we analyse the behaviour of quantum mobile agents operating
with non-adaptive and adaptive strategies which can be employed in this
scenario. We introduce the notion of node visiting suitable for
analysing quantum superpositions of states by distinguishing between
visiting and attaining a position. We show that without a proper model
of adaptiveness, it is not possible for the party representing the
distraction in the sense of direction, to obtain the results analogous
to the classical case. Moreover, with additional control resources the
total number of attained positions is maintained and the number of
visited positions is strictly limited.

**CTC assisted PR box type correlation can lead to
signaling**
(pp1251-1260)

Indranil
Chakrabarty, Tanumoy Pramanik, Arun K Pati, and Pankaj Agrawal

It is known that there exist non-local correlations that respect
no-signaling criterion, but violate Bell-type inequalities more than
quantum-mechanical correlations. Such super quantum correlations were
introduced as the Popescu-Rohrlich (PR) box. We consider such non-local
boxes with two/three inputs and two/three outputs. We show that these
super quantum correlations can lead to signaling when at least one of
the input bit has access to a word line along a closed time-like curve.