1,356 research outputs found

### The Power of LOCCq State Transformations

Reversible state transformations under entanglement non-increasing operations
give rise to entanglement measures. It is well known that asymptotic local
operations and classical communication (LOCC) are required to get a simple
operational measure of bipartite pure state entanglement. For bipartite mixed
states and multipartite pure states it is likely that a more powerful class of
operations will be needed. To this end \cite{BPRST01} have defined more
powerful versions of state transformations (or reducibilities), namely LOCCq
(asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC
(asymptotic LOCC with catalysis). In this paper we show that {\em LOCCq state
transformations are only as powerful as asymptotic LOCC state transformations}
for multipartite pure states. We first generalize the concept of entanglement
gambling from two parties to multiple parties: any pure multipartite entangled
state can be transformed to an EPR pair shared by some pair of parties and that
any irreducible $m$ $(m\ge 2)$ party pure state can be used to create any other
state (pure or mixed), using only local operations and classical communication
(LOCC). We then use this tool to prove the result. We mention some applications
of multipartite entanglement gambling to multipartite distillability and to
characterizations of multipartite minimal entanglement generating sets. Finally
we discuss generalizations of this result to mixed states by defining the class
of {\em cat distillable states}

### A Measure of Stregth of an Unextendible Product Basis

A notion of strength of an unextendible product basis is introduced and a
quantitative measure for it is suggested with a view to providing an indirect
measure for the bound entanglement of formation of the bound entangled mixed
state associated with an unextendible product basis.Comment: 4 pages, Latex, 1 figure, remarks, criticisms welcom

### The Nature and Location of Quantum Information

Quantum information is defined by applying the concepts of ordinary (Shannon)
information theory to a quantum sample space consisting of a single framework
or consistent family. A classical analogy for a spin-half particle and other
arguments show that the infinite amount of information needed to specify a
precise vector in its Hilbert space is not a measure of the information carried
by a quantum entity with a $d$-dimensional Hilbert space; the latter is,
instead, bounded by log d bits (1 bit per qubit). The two bits of information
transmitted in dense coding are located not in one but in the correlation
between two qubits, consistent with this bound. A quantum channel can be
thought of as a "structure" or collection of frameworks, and the physical
location of the information in the individual frameworks can be used to
identify the location of the channel. Analysis of a quantum circuit used as a
model of teleportation shows that the location of the channel depends upon
which structure is employed; for ordinary teleportation it is not (contrary to
Deutsch and Hayden) present in the two bits resulting from the Bell-basis
measurement, but in correlations of these with a distant qubit. In neither
teleportation nor dense coding does information travel backwards in time, nor
is it transmitted by nonlocal (superluminal) influences. It is (tentatively)
proposed that all aspects of quantum information can in principle be understood
in terms of the (basically classical) behavior of information in a particular
framework, along with the framework dependence of this information.Comment: Latex 29 pages, uses PSTricks for figure

### Quantum Communication Protocol Employing Weak Measurements

We propose a communication protocol exploiting correlations between two
events with a definite time-ordering: a) the outcome of a {\em weak
measurement} on a spin, and b) the outcome of a subsequent ordinary measurement
on the spin. In our protocol, Alice, first generates a "code" by performing
weak measurements on a sample of N spins.
The sample is sent to Bob, who later performs a post-selection by measuring
the spin along either of two certain directions. The results of the
post-selection define the "key', which he then broadcasts publicly. Using both
her previously generated code and this key, Alice is able to infer the {\em
direction} chosen by Bob in the post-selection. Alternatively, if Alice
broadcasts publicly her code, Bob is able to infer from the code and the key
the direction chosen by Alice for her weak measurement. Two possible
experimental realizations of the protocols are briefly mentioned.Comment: 5 pages, Revtex, 1 figure. A second protocol is added, where by a
similar set of weak measurement Alice can send, instead of receiving, a
message to Bob. The security question for the latter protocol is discusse

### New classes of n-copy undistillable quantum states with negative partial transposition

The discovery of entangled quantum states from which one cannot distill pure
entanglement constitutes a fundamental recent advance in the field of quantum
information. Such bipartite bound-entangled (BE) quantum states \emph{could}
fall into two distinct categories: (1) Inseparable states with positive partial
transposition (PPT), and (2) States with negative partial transposition (NPT).
While the existence of PPT BE states has been confirmed, \emph{only one} class
of \emph{conjectured} NPT BE states has been discovered so far. We provide
explicit constructions of a variety of multi-copy undistillable NPT states, and
conjecture that they constitute families of NPT BE states. For example, we show
that for every pure state of Schmidt rank greater than or equal to three, one
can construct n-copy undistillable NPT states, for any $n\geq1$. The abundance
of such conjectured NPT BE states, we believe, considerably strengthens the
notion that being NPT is only a necessary condition for a state to be
distillable.Comment: Latex, 10 page

### Entanglement required in achieving entanglement-assisted channel capacities

Entanglement shared between the two ends of a quantum communication channel
has been shown to be a useful resource in increasing both the quantum and
classical capacities for these channels. The entanglement-assisted capacities
were derived assuming an unlimited amount of shared entanglement per channel
use. In this paper, bounds are derived on the minimum amount of entanglement
required per use of a channel, in order to asymptotically achieve the capacity.
This is achieved by introducing a class of entanglement-assisted quantum codes.
Codes for classes of qubit channels are shown to achieve the quantum
entanglement-assisted channel capacity when an amount of shared entanglement
per channel given by, E = 1 - Q_E, is provided. It is also shown that for very
noisy channels, as the capacities become small, the amount of required
entanglement converges for the classical and quantum capacities.Comment: 9 pages, 2 figures, RevTex

### Quantum identification system

A secure quantum identification system combining a classical identification
procedure and quantum key distribution is proposed. Each identification
sequence is always used just once and new sequences are ``refuelled'' from a
shared provably secret key transferred through the quantum channel. Two
identification protocols are devised. The first protocol can be applied when
legitimate users have an unjammable public channel at their disposal. The
deception probability is derived for the case of a noisy quantum channel. The
second protocol employs unconditionally secure authentication of information
sent over the public channel, and thus it can be applied even in the case when
an adversary is allowed to modify public communications. An experimental
realization of a quantum identification system is described.Comment: RevTeX, 4 postscript figures, 9 pages, submitted to Physical Review

### Activating bound entanglement in multi-particle systems

We analyze the existence of activable bound entangled states in
multi-particle systems. We first give a series of examples which illustrate
some different ways in which bound entangled states can be activated by letting
some of the parties to share maximally entangled states. Then, we derive
necessary conditions for a state to be distillable as well as to be activable.
These conditions turn out to be also sufficient for a certain family of
multi-qubit states. We use these results to explicitely to construct states
displaying novel properties related to bound entanglement and its activation.Comment: 8 pages, 3 figure

### Entanglement sharing among qudits

Consider a system consisting of n d-dimensional quantum particles (qudits),
and suppose that we want to optimize the entanglement between each pair. One
can ask the following basic question regarding the sharing of entanglement:
what is the largest possible value Emax(n,d) of the minimum entanglement
between any two particles in the system? (Here we take the entanglement of
formation as our measure of entanglement.) For n=3 and d=2, that is, for a
system of three qubits, the answer is known: Emax(3,2) = 0.550. In this paper
we consider first a system of d qudits and show that Emax(d,d) is greater than
or equal to 1. We then consider a system of three particles, with three
different values of d. Our results for the three-particle case suggest that as
the dimension d increases, the particles can share a greater fraction of their
entanglement capacity.Comment: 4 pages; v2 contains a new result for 3 qudits with d=

### A Necessary And Sufficient Condition of Distillability with unite fidelity from Finite Copies of a Mixed State: The Most Efficient Purification Protocol

It is well known that any entangled mixed state in $2\otimes 2$ systems can
be purified via infinite copies of the mixed state. But can one distill a pure
maximally entangled state from finite copies of a mixed state in any bipartite
system by local operation and classical communication? This is more meaningful
in practical application. We give a necessary and sufficient condition of this
distillability. This condition can be expressed as: there exists
distillable-subspaces. According to this condition, one can judge whether a
mixed state is distillable or not easily. We also analyze some properties of
distillable-subspaces, and discuss the most efficient purification protocols.
Finally, we discuss the distillable enanglement of two-quibt system for the
case of finite copies.Comment: a revised versio

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