913 research outputs found
The private capacity of quantum channels is not additive
Recently there has been considerable activity on the subject of additivity of
various quantum channel capacities. Here, we construct a family of channels
with sharply bounded classical, hence private capacity. On the other hand,
their quantum capacity when combined with a zero private (and zero quantum)
capacity erasure channel, becomes larger than the previous classical capacity.
As a consequence, we can conclude for the first time that the classical
private capacity is non-additive. In fact, in our construction even the quantum
capacity of the tensor product of two channels can be greater than the sum of
their individual classical private capacities.
We show that this violation occurs quite generically: every channel can be
embedded into our construction, and a violation occurs whenever the given
channel has larger entanglement assisted quantum capacity than (unassisted)
classical capacity.Comment: 4+4 pages, 2 eps figures. V2 has title and abstract changed; its new
structure reflects the final version of a main paper plus appendices
containing mathematical detail
Schumacher's quantum data compression as a quantum computation
An explicit algorithm for performing Schumacher's noiseless compression of
quantum bits is given. This algorithm is based on a combinatorial expression
for a particular bijection among binary strings. The algorithm, which adheres
to the rules of reversible programming, is expressed in a high-level pseudocode
language. It is implemented using two- and three-bit primitive
reversible operations, where is the length of the qubit strings to be
compressed. Also, the algorithm makes use of auxiliary qubits; however,
space-saving techniques based on those proposed by Bennett are developed which
reduce this workspace to while increasing the running time by
less than a factor of two.Comment: 37 pages, no figure
Effects of detector efficiency mismatch on security of quantum cryptosystems
We suggest a type of attack on quantum cryptosystems that exploits variations
in detector efficiency as a function of a control parameter accessible to an
eavesdropper. With gated single-photon detectors, this control parameter can be
the timing of the incoming pulse. When the eavesdropper sends short pulses
using the appropriate timing so that the two gated detectors in Bob's setup
have different efficiencies, the security of quantum key distribution can be
compromised. Specifically, we show for the Bennett-Brassard 1984 (BB84)
protocol that if the efficiency mismatch between 0 and 1 detectors for some
value of the control parameter gets large enough (roughly 15:1 or larger), Eve
can construct a successful faked-states attack causing a quantum bit error rate
lower than 11%. We also derive a general security bound as a function of the
detector sensitivity mismatch for the BB84 protocol. Experimental data for two
different detectors are presented, and protection measures against this attack
are discussed.Comment: v3: identical to the journal version. However, after publication we
have discovered that Eq. 11 is incorrect: the available bit rate after
privacy amplification is reduced even in the case (QBER)=0 [see Quant. Inf.
Comp. 7, 73 (2007)
Multidimensional reconciliation for continuous-variable quantum key distribution
We propose a method for extracting an errorless secret key in a
continuous-variable quantum key distribution protocol, which is based on
Gaussian modulation of coherent states and homodyne detection. The crucial
feature is an eight-dimensional reconciliation method, based on the algebraic
properties of octonions. Since the protocol does not use any postselection, it
can be proven secure against arbitrary collective attacks, by using
well-established theorems on the optimality of Gaussian attacks. By using this
new coding scheme with an appropriate signal to noise ratio, the distance for
secure continuous-variable quantum key distribution can be significantly
extended.Comment: 8 pages, 3 figure
Monogamy and polygamy for multi-qubit entanglement using R\'enyi entropy
Using R\'enyi- entropy to quantify bipartite entanglement, we prove
monogamy of entanglement in multi-qubit systems for . We also
conjecture a polygamy inequality of multi-qubit entanglement with strong
numerical evidence for with
.Comment: 19 pages, 2 figure
Entropic bounds on coding for noisy quantum channels
In analogy with its classical counterpart, a noisy quantum channel is
characterized by a loss, a quantity that depends on the channel input and the
quantum operation performed by the channel. The loss reflects the transmission
quality: if the loss is zero, quantum information can be perfectly transmitted
at a rate measured by the quantum source entropy. By using block coding based
on sequences of n entangled symbols, the average loss (defined as the overall
loss of the joint n-symbol channel divided by n, when n tends to infinity) can
be made lower than the loss for a single use of the channel. In this context,
we examine several upper bounds on the rate at which quantum information can be
transmitted reliably via a noisy channel, that is, with an asymptotically
vanishing average loss while the one-symbol loss of the channel is non-zero.
These bounds on the channel capacity rely on the entropic Singleton bound on
quantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we
analyze the Singleton bounds when the noisy quantum channel is supplemented
with a classical auxiliary channel.Comment: 20 pages RevTeX, 10 Postscript figures. Expanded Section II, added 1
figure, changed title. To appear in Phys. Rev. A (May 98
Quantum conditional operator and a criterion for separability
We analyze the properties of the conditional amplitude operator, the quantum
analog of the conditional probability which has been introduced in
[quant-ph/9512022]. The spectrum of the conditional operator characterizing a
quantum bipartite system is invariant under local unitary transformations and
reflects its inseparability. More specifically, it is shown that the
conditional amplitude operator of a separable state cannot have an eigenvalue
exceeding 1, which results in a necessary condition for separability. This
leads us to consider a related separability criterion based on the positive map
, where is an Hermitian operator. Any
separable state is mapped by the tensor product of this map and the identity
into a non-negative operator, which provides a simple necessary condition for
separability. In the special case where one subsystem is a quantum bit,
reduces to time-reversal, so that this separability condition is
equivalent to partial transposition. It is therefore also sufficient for
and systems. Finally, a simple connection between this
map and complex conjugation in the "magic" basis is displayed.Comment: 19 pages, RevTe
Quantum Channel Capacity of Very Noisy Channels
We present a family of additive quantum error-correcting codes whose
capacities exceeds that of quantum random coding (hashing) for very noisy
channels. These codes provide non-zero capacity in a depolarizing channel for
fidelity parameters when . Random coding has non-zero capacity
only for ; by analogy to the classical Shannon coding limit, this
value had previously been conjectured to be a lower bound. We use the method
introduced by Shor and Smolin of concatenating a non-random (cat) code within a
random code to obtain good codes. The cat code with block size five is shown to
be optimal for single concatenation. The best known multiple-concatenated code
we found has a block size of 25. We derive a general relation between the
capacity attainable by these concatenation schemes and the coherent information
of the inner code states.Comment: 31 pages including epsf postscript figures. Replaced to correct
important typographical errors in equations 36, 37 and in tex
Classical, quantum and total correlations
We discuss the problem of separating consistently the total correlations in a
bipartite quantum state into a quantum and a purely classical part. A measure
of classical correlations is proposed and its properties are explored.Comment: 10 pages, 3 figure
Quantum key distribution without alternative measurements
Entanglement swapping between Einstein-Podolsky-Rosen (EPR) pairs can be used
to generate the same sequence of random bits in two remote places. A quantum
key distribution protocol based on this idea is described. The scheme exhibits
the following features. (a) It does not require that Alice and Bob choose
between alternative measurements, therefore improving the rate of generated
bits by transmitted qubit. (b) It allows Alice and Bob to generate a key of
arbitrary length using a single quantum system (three EPR pairs), instead of a
long sequence of them. (c) Detecting Eve requires the comparison of fewer bits.
(d) Entanglement is an essential ingredient. The scheme assumes reliable
measurements of the Bell operator.Comment: REVTeX, 5 pages, 2 figures. Published version with some comment
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