31,264 research outputs found
When only two thirds of the entanglement can be distilled
We provide an example of distillable bipartite mixed state such that, even in
the asymptotic limit, more pure-state entanglement is required to create it
than can be distilled from it. Thus, we show that the irreversibility in the
processes of formation and distillation of bipartite states, recently proved in
[G. Vidal, J.I. Cirac, Phys. Rev. Lett. 86, (2001) 5803-5806], is not limited
to bound-entangled states.Comment: 4 pages, revtex, 1 figur
Quantifying nonorthogonality
An exploratory approach to the possibility of analyzing nonorthogonality as a
quantifiable property is presented. Three different measures for the
nonorthogonality of pure states are introduced, and one of these measures is
extended to single-particle density matrices using methods that are similar to
recently introduced techniques for quantifying entanglement. Several
interesting special cases are considered. It is pointed out that a measure of
nonorthogonality can meaningfully be associated with a single mixed quantum
state. It is then shown how nonorthogonality can be unlocked with classical
information; this analysis reveals interesting inequalities and points to a
number of connections between nonorthogonality and entanglement.Comment: Accepted for publication in Phys. Rev.
A method of enciphering quantum states
In this paper, we propose a method of enciphering quantum states of two-state
systems (qubits) for sending them in secrecy without entangled qubits shared by
two legitimate users (Alice and Bob). This method has the following two
properties. First, even if an eavesdropper (Eve) steals qubits, she can extract
information from them with certain probability at most. Second, Alice and Bob
can confirm that the qubits are transmitted between them correctly by measuring
a signature. If Eve measures m qubits one by one from n enciphered qubits and
sends alternative ones (the Intercept/Resend attack), a probability that Alice
and Bob do not notice Eve's action is equal to (3/4)^m or less. Passwords for
decryption and the signature are given by classical binary strings and they are
disclosed through a public channel. Enciphering classical information by this
method is equivalent to the one-time pad method with distributing a classical
key (random binary string) by the BB84 protocol. If Eve takes away qubits,
Alice and Bob lose the original quantum information. If we apply our method to
a state in iteration, Eve's success probability decreases exponentially. We
cannot examine security against the case that Eve makes an attack with using
entanglement. This remains to be solved in the future.Comment: 21 pages, Latex2e, 10 epsf figures. v2: 22 pages, added two
references, several clarifying sentences are added in Sec. 5, typos
corrected, a new proof is provided in Appendix A and it is shorter than the
old one. v3: 23 pages, one section is adde
Remote State Preparation
Quantum teleportation uses prior entanglement and forward classical
communication to transmit one instance of an unknown quantum state. Remote
state preparation (RSP) has the same goal, but the sender knows classically
what state is to be transmitted. We show that the asymptotic classical
communication cost of RSP is one bit per qubit - half that of teleportation -
and becomes even less when transmitting part of a known entangled state. We
explore the tradeoff between entanglement and classical communication required
for RSP, and discuss RSP capacities of general quantum channels.Comment: 4 pages including 1 epsf figure; v3 has an additional author and
discusses relation to work of Devetak and Berger (quant-ph/0102123); v4
improves low-entanglement protocols without back communication to perform as
well as low-entanglement protocols with back communication; v5 (journal
version) has a few small change
Quantum communication without alignment using multiple-qubit single-photon states
We propose a scheme for encoding logical qubits in a subspace protected
against collective rotations around the propagation axis using the polarization
and transverse spatial degrees of freedom of single photons. This encoding
allows for quantum key distribution without the need of a shared reference
frame. We present methods to generate entangled states of two logical qubits
using present day down-conversion sources and linear optics, and show that the
application of these entangled logical states to quantum information schemes
allows for alignment-free tests of Bell's inequalities, quantum dense coding
and quantum teleportation
Irreversibility in asymptotic manipulations of entanglement
We show that the process of entanglement distillation is irreversible by
showing that the entanglement cost of a bound entangled state is finite. Such
irreversibility remains even if extra pure entanglement is loaned to assist the
distillation process.Comment: RevTex, 3 pages, no figures Result on indistillability of PPT states
under pure entanglement catalytic LOCC adde
On the origin of noisy states whose teleportation fidelity can be enhanced through dissipation
Recently Badziag \emph{et al.} \cite{badziag} obtained a class of noisy
states whose teleportation fidelity can be enhanced by subjecting one of the
qubits to dissipative interaction with the environment via amplitude damping
channel (ADC). We show that such noisy states result while sharing the states
(| \Phi ^{\pm}> =\frac{1}{\sqrt{2}}(| 00> \pm | 11>)) across ADC. We also show
that under similar dissipative interactions different Bell states give rise to
noisy entangled states that are qualitatively very different from each other in
the sense, only the noisy entangled states constructed from the Bell states (|
\Phi ^{\pm}>) can \emph{}be made better sometimes by subjecting the unaffected
qubit to a dissipative interaction with the environment. Importantly if the
noisy state is non teleporting then it can always be made teleporting with this
prescription. We derive the most general restrictions on improvement of such
noisy states assuming that the damping parameters being different for both the
qubits. However this curious prescription does not work for the noisy entangled
states generated from (| \Psi ^{\pm}> =\frac{1}{\sqrt{2}}(| 01> \pm | 10>)).
This shows that an apriori knowledge of the noisy channel might be helpful to
decide which Bell state needs to be shared between Alice and Bob. \emph{}Comment: Latex, 18 pages: Revised version with a new result. Submitted to PR
Generalized remote state preparation: Trading cbits, qubits and ebits in quantum communication
We consider the problem of communicating quantum states by simultaneously
making use of a noiseless classical channel, a noiseless quantum channel and
shared entanglement. We specifically study the version of the problem in which
the sender is given knowledge of the state to be communicated. In this setting,
a trade-off arises between the three resources, some portions of which have
been investigated previously in the contexts of the quantum-classical trade-off
in data compression, remote state preparation and superdense coding of quantum
states, each of which amounts to allowing just two out of these three
resources. We present a formula for the triple resource trade-off that reduces
its calculation to evaluating the data compression trade-off formula. In the
process, we also construct protocols achieving all the optimal points. These
turn out to be achievable by trade-off coding and suitable time-sharing between
optimal protocols for cases involving two resources out of the three mentioned
above.Comment: 15 pages, 2 figures, 1 tabl
Mixed State Entanglement and Quantum Error Correction
Entanglement purification protocols (EPP) and quantum error-correcting codes
(QECC) provide two ways of protecting quantum states from interaction with the
environment. In an EPP, perfectly entangled pure states are extracted, with
some yield D, from a mixed state M shared by two parties; with a QECC, an arbi-
trary quantum state can be transmitted at some rate Q through a
noisy channel without degradation. We prove that an EPP involving one-
way classical communication and acting on mixed state (obtained
by sharing halves of EPR pairs through a channel ) yields a QECC on
with rate , and vice versa. We compare the amount of entanglement
E(M) required to prepare a mixed state M by local actions with the amounts
and that can be locally distilled from it by EPPs using one-
and two-way classical communication respectively, and give an exact expression
for when is Bell-diagonal. While EPPs require classical communica-
tion, QECCs do not, and we prove Q is not increased by adding one-way classical
communication. However, both D and Q can be increased by adding two-way com-
munication. We show that certain noisy quantum channels, for example a 50%
depolarizing channel, can be used for reliable transmission of quantum states
if two-way communication is available, but cannot be used if only one-way com-
munication is available. We exhibit a family of codes based on universal hash-
ing able toachieve an asymptotic (or ) of 1-S for simple noise models,
where S is the error entropy. We also obtain a specific, simple 5-bit single-
error-correcting quantum block code. We prove that {\em iff} a QECC results in
high fidelity for the case of no error the QECC can be recast into a form where
the encoder is the matrix inverse of the decoder.Comment: Resubmission with various corrections and expansions. See also
http://vesta.physics.ucla.edu/~smolin/ for related papers and information. 82
pages latex including 19 postscript figures included using psfig macro
Negative entropy and information in quantum mechanics
A framework for a quantum mechanical information theory is introduced that is
based entirely on density operators, and gives rise to a unified description of
classical correlation and quantum entanglement. Unlike in classical (Shannon)
information theory, quantum (von Neumann) conditional entropies can be negative
when considering quantum entangled systems, a fact related to quantum
non-separability. The possibility that negative (virtual) information can be
carried by entangled particles suggests a consistent interpretation of quantum
informational processes.Comment: 4 pages RevTeX, 2 figures. Expanded discussion of quantum
teleportation and superdense coding, and minor corrections. To appear in
Phys. Rev. Let
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