MIXED-STATE ENTANGLEMENT IN THE LIGHT OF PURE-STATE ENTANGLEMENT CONSTRAINED BY SUPERSELECTION RULES

2005 ◽  
Author(s):  
STEPHEN D. BARTLETT ◽  
HOWARD. M. WISEMAN ◽  
ROBERT W. SPEKKENS ◽  
ANDREW C. DOHERTY
Keyword(s):  
Mixed State ◽  
Pure State

Probabilistic secret sharing through noise quantum channe

2012 ◽  
Vol 12 (3&4) ◽  
pp. 253-261
Author(s):  
Satyabrata Adhikari ◽  
Indranil Chakrabarty ◽  
Pankaj Agrawal
Keyword(s):  
Quantum Information ◽  
Secret Sharing ◽  
Mixed State ◽  
Pure State ◽  
Noisy Channel ◽  
Noisy Channels ◽  
Superdense Coding ◽  
Classical Information ◽  
Phase Damping ◽  
Realistic Situation

In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.

Quantum Dynamics and Entropy in a Single-Cooper-Pair Box with a Single-Mode Cavity Field

2003 ◽  
Vol 17 (14) ◽  
pp. 2699-2713 ◽  
Author(s):  
Meng Zhang ◽  
Jian Zou ◽  
Bin Shao
Keyword(s):  
Mixed State ◽  
Pure State ◽  
Quantum Dynamics ◽  
Cooper Pair ◽  
Single Mode ◽  
Quantum Entropy ◽  
Cavity Field ◽  
Cooper Pair Box ◽  
Quantized Field ◽  
Single Mode Cavity

We consider a single-Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field. We assume that the box is initially in a mixed state, and investigate the quantum dynamics of the Cooper-pair box and show that the collapse and revival phenomenon can exist in this system. We also study the quantum entropy of the single-Cooper-pair box and discuss the effects of the different parameters on this quantum entropy. We find that the box, which is initially in a mixed state, may evolve into an almost pure state.

scholarly journals SOME FEATURES OF THE STATE-SPACE TRAJECTORIES FOLLOWED BY ROBUST ENTANGLED FOUR-QUBIT STATES DURING DECOHERENCE

2010 ◽  
Vol 08 (03) ◽  
pp. 505-515 ◽  
Author(s):  
A. P. MAJTEY ◽  
A. BORRAS ◽  
A. R. PLASTINO ◽  
M. CASAS ◽  
A. PLASTINO
Keyword(s):  
State Space ◽  
Recent Work ◽  
Mixed State ◽  
Pure State ◽  
The State ◽  
Time Dependent ◽  
Space Trajectories ◽  
Geometrical Features ◽  
Initial States ◽  
Qubit States

In a recent work (Borras et al., Phys. Rev. A79 (2009) 022108), we have determined, for various decoherence channels, four-qubit initial states exhibiting the most robust possible entanglement. Here, we explore some geometrical features of the trajectories in state space generated by the decoherence process, connecting the initially robust pure state with the completely decohered mixed state obtained at the end of the evolution. We characterize these trajectories by recourse to the distance between the concomitant time-dependent mixed state and different reference states.

scholarly journals Impossibility of Distinguishing Two Preparations for a Pure State from No-signaling

Quanta ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 16-21
Author(s):  
Arun K. Pati
Keyword(s):  
Quantum Theory ◽  
Infinite Number ◽  
Mixed State ◽  
Physical System ◽  
Pure State ◽  
Entangled State ◽  
No Signaling

A pure state of a physical system can be prepared in an infinite number of ways. Quantum theory dictates that given a pure state of a physical system it is impossible to distinguish two preparation procedures. Here, we show that the impossibility of distinguishing two preparation procedures for the same pure state follows from the no-signaling principle. Extending this result for a pure bipartite entangled state entails that the impossibility of distinguishing two preparation procedures for a mixed state follows from the impossibility of distinguishing two preparations for a pure bipartite state.Quanta 2020; 9: 16–21.

MIXED-STATE ENTANGLEMENT IN THE LIGHT OF PURE-STATE ENTANGLEMENT CONSTRAINED BY SUPERSELECTION RULES

2005 ◽  
Vol 03 (supp01) ◽  
pp. 145-153
Author(s):  
STEPHEN D. BARTLETT ◽  
HOWARD. M. WISEMAN ◽  
ROBERT W. SPEKKENS ◽  
ANDREW C. DOHERTY
Keyword(s):  
Mixed State ◽  
Pure State ◽  
Entangled States ◽  
Quantum Operations ◽  
Local Quantum ◽  
Bound Entanglement ◽  
Quantum Optical

We show that the classification of bi-partite pure entangled states when local quantum operations are restricted, e.g., constrained by local superselection rules, yields a structure that is analogous in many respects to that of mixed-state entanglement, including such exotic phenomena as bound entanglement and activation. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. Specifically, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

scholarly journals Derivation of the robustness from the concurrence

2021 ◽  
pp. 2150166
Author(s):  
Yu. S. Krynytskyi ◽  
A. R. Kuzmak
Keyword(s):  
Mixed State ◽  
Pure State ◽  
Quantitative Measure ◽  
Exact Expression ◽  
Entangled State ◽  
Special Cases ◽  
Qubit States

Adding the maximally mixed state with some weight to the entanglement system leads to disentanglement of the latter. For each predefined entangled state there exists a minimal value of this weight for which the system loses its entanglement properties. These values were proposed to be used as a quantitative measure of entanglement called robustness [G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999)]. Using the concurrence, we propose the derivation of this measure for the system of two-qubit. Namely, for a two-qubit pure state, an exact expression of robustness is obtained. Finally, in the same way, the robustness of special cases of mixed two-qubit states is calculated.

scholarly journals Convex hulls of varieties and entanglement measures based on the roof construction

2007 ◽  
Vol 7 (3) ◽  
pp. 209-227
Author(s):  
T.J. Osborne
Keyword(s):  
Convex Hull ◽  
Quantum Entanglement ◽  
Mixed State ◽  
Pure State ◽  
Convex Hulls ◽  
Algebraic Varieties ◽  
Implicit Representation ◽  
Entanglement Measures ◽  
State Extension

In this paper we study the problem of calculating the convex hull of certain affine algebraic varieties. As we explain, the motivation for considering this problem is that certain pure-state measures of quantum entanglement, which we call \emph{polynomial entanglement measures}, can be represented as affine algebraic varieties. We consider the evaluation of certain mixed-state extensions of these polynomial entanglement measures, namely \emph{convex and concave roofs}. We show that the evaluation of a roof-based mixed-state extension is equivalent to calculating a hyperplane which is multiply tangent to the variety in a number of places equal to the number of terms in an optimal decomposition for the measure. In this way we provide an \emph{implicit} representation of optimal decompositions for mixed-state entanglement measures based on the roof construction.

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