Markov Quantum Feedback Control Based on Homodyne Measurement of a Two-Qubit System

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -spin maximal entanglement.

Section: The Entanglement Propertymentioning

confidence: 99%

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

Zhu¹

2014

“…Now, let us study the entanglement property of the MPS, the key quantity of quantum information theory [14][15][16][17], in detail. There are many kinds of methods to measure entanglement, such as the quantification characteristic function of quantum nonlocality [18], Bell inequality [19,20], quantum discord [21], averaged entropy [22] and so on.…”

Section: The Entanglement Propertymentioning

confidence: 99%

Quantum phase transitions in matrix product states of one-dimensional spin-½ chains

Zhu

2014

For the matrix product system of a one-dimensional spin-½ chain, we present a new model of quantum phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψa〉 = |1…1〉 representing all particles spin up and |Ψb〉 = |0…0〉 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where the two phases coexist equally, which is described by the so-called N-qubit maximally entangled GHZ state . At the critical point, the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.

Quantum phase transitions about parity breaking in matrix product systems

Zhu¹

2011

According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.