10 research outputs found
Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication
The error threshold for fault tolerant quantum computation with concatenated
encoding of qubits is penalized by internal communication overhead. Many
quantum computation proposals rely on nearest-neighbour communication, which
requires excess gate operations. For a qubit stripe with a width of L+1
physical qubits implementing L levels of concatenation, we find that the error
threshold of 2.1x10^-5 without any communication burden is reduced to 1.2x10^-7
when gate errors are the dominant source of error. This ~175X penalty in error
threshold translates to an ~13X penalty in the amplitude and timing of gate
operation control pulses.Comment: minor correctio
Factorizations and Physical Representations
A Hilbert space in M dimensions is shown explicitly to accommodate
representations that reflect the prime numbers decomposition of M.
Representations that exhibit the factorization of M into two relatively prime
numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)),
and related representations termed representations (together with
their conjugates) are analysed, as well as a representation that exhibits the
complete factorization of M. In this latter representation each quantum number
varies in a subspace that is associated with one of the prime numbers that make
up M
Controlling passively-quenched single photon detectors by bright light
Single photon detectors based on passively-quenched avalanche photodiodes can
be temporarily blinded by relatively bright light, of intensity less than a
nanowatt. I describe a bright-light regime suitable for attacking a quantum key
distribution system containing such detectors. In this regime, all single
photon detectors in the receiver Bob are uniformly blinded by continuous
illumination coming from the eavesdropper Eve. When Eve needs a certain
detector in Bob to produce a click, she modifies polarization (or other
parameter used to encode quantum states) of the light she sends to Bob such
that the target detector stops receiving light while the other detector(s)
continue to be illuminated. The target detector regains single photon
sensitivity and, when Eve modifies the polarization again, produces a single
click. Thus, Eve has full control of Bob and can do a successful
intercept-resend attack. To check the feasibility of the attack, 3 different
models of passively-quenched detectors have been tested. In the experiment, I
have simulated the intensity diagrams the detectors would receive in a real
quantum key distribution system under attack. Control parameters and side
effects are considered. It appears that the attack could be practically
possible.Comment: Experimental results from a third detector model added. Minor
corrections and edits made. 11 pages, 10 figure
Pauli Diagonal Channels Constant on Axes
We define and study the properties of channels which are analogous to unital
qubit channels in several ways. A full treatment can be given only when the
dimension d is a prime power, in which case each of the (d+1) mutually unbiased
bases (MUB) defines an axis. Along each axis the channel looks like a
depolarizing channel, but the degree of depolarization depends on the axis.
When d is not a prime power, some of our results still hold, particularly in
the case of channels with one symmetry axis. We describe the convex structure
of this class of channels and the subclass of entanglement breaking channels.
We find new bound entangled states for d = 3.
For these channels, we show that the multiplicativity conjecture for maximal
output p-norm holds for p=2. We also find channels with behavior not exhibited
by unital qubit channels, including two pairs of orthogonal bases with equal
output entropy in the absence of symmetry. This provides new numerical evidence
for the additivity of minimal output entropy
Optimality of private quantum channels
We addressed the question of optimality of private quantum channels. We have
shown that the Shannon entropy of the classical key necessary to securely
transfer the quantum information is lower bounded by the entropy exchange of
the private quantum channel and von Neumann entropy of the ciphertext
state . Based on these bounds we have shown that decomposition
of private quantum channels into orthogonal unitaries (if exists) is optimizing
the entropy. For non-ancillary single qubit PQC we have derived the optimal
entropy for arbitrary set of plaintexts. In particular, we have shown that
except when the (closure of the) set of plaintexts contains all states, one bit
key is sufficient. We characterized and analyzed all the possible single qubit
private quantum channels for arbitrary set of plaintexts. For the set of
plaintexts consisting of all qubit states we have characterized all possible
approximate private quantum channels and we have derived the relation between
the security parameter and the corresponding minimal entropy.Comment: no commen
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