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Register a new userMaximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
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Two important results of quantum physics are the textit{no-cloning} theorem and the textit{monogamy of entanglement}. The former forbids the creation of an independent and identical copy of an arbitrary unknown quantum state and the latter restricts the shareability of quantum entanglement among multiple quantum systems. For distinguishable particles, one of these results imply the other. In this Letter, we show that in qubit systems with indistinguishable particles (where each particle cannot be addressed individually), a maximum violation of the monogamy of entanglement is possible by the measures that are monogamous for distinguishable particles. To derive this result, we formulate the degree of freedom trace-out rule for indistinguishable particles corresponding to a spatial location where each degree of freedom might be entangled with the other degrees of freedom. Our result removes the restriction on the shareability of quantum entanglement for indistinguishable particles, without contradicting the no-cloning theorem.
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Using an operational definition we quantify the entanglement, $E_P$, between two parties who share an arbitrary pure state of $N$ indistinguishable particles. We show that $E_P leq E_M$, where $E_M$ is the bipartite entanglement calculated from the mode-occupation representation. Unlike $E_M$, $E_P$ is {em super-additive}. For example, $E_P =0$ for any single-particle state, but the state $ket{1}ket{1}$, where both modes are split between the two parties, has $E_P = 1/2$. We discuss how this relates to quantum correlations between particles, for both fermions and bosons.
We present an investigation of many-particle quantum walks in systems of non-interacting distinguishable particles. Along with a redistribution of the many-particle density profile we show that the collective evolution of the many-particle system resembles the single-particle quantum walk evolution when the number of steps is greater than the number of particles in the system. For non-uniform initial states we show that the quantum walks can be effectively used to separate the basis states of the particle in position space and grouping like state together. We also discuss a two-particle quantum walk on a two- dimensional lattice and demonstrate an evolution leading to the localization of both particles at the center of the lattice. Finally we discuss the outcome of a quantum walk of two indistinguishable particles interacting at some point during the evolution.
The monogamy of quantum entanglement captures the property of limitation in the distribution of entanglement. Various monogamy relations exist for different entanglement measures that are important in quantum information processing. Our goal in this work is to propose a general monogamy inequality for all entanglement measures on entangled qubit systems. The present result provide a unified model for various entanglement measures including the concurrence, the negativity, the entanglement of formation, Tsallis-q entropy, Renyi-q entropy, and Unified-(q,s) entropy. We then proposed tightened monogamy inequalities for multipartite systems. We finally prove a generic result for the tangle of high-dimensional entangled states to show the distinct feature going beyond qubit systems. These results are useful for exploring the entanglement theory, quantum information processing and secure quantum communication.
We introduce a framework for the construction of completely positive maps for subsystems of indistinguishable fermionic particles. In this scenario, the initial global state is always correlated, and it is not possible to tell system and environment apart. Nonetheless, a reduced map in the operator sum representation is possible for some sets of states where the only non-classical correlation present is exchange.
It is generally believed that dispersive polarimetric detection of collective angular momentum in large atomic spin systems gives rise to: squeezing in the measured observable, anti-squeezing in a conjugate observable, and collective spin eigenstates in the long-time limit (provided that decoherence is suitably controlled). We show that such behavior only holds when the particles in the ensemble cannot be spatially distinguished-- even in principle-- regardless of whether the measurement is only sensitive to collective observables. While measuring a cloud of spatially-distinguishable spin-1/2 particles does reduce the uncertainty in the measured spin component, it generates neither squeezing nor anti-squeezing. The steady state of the measurement is highly mixed, albeit with a well-defined value of the measured collective angular momentum observable.
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